FRBSF Economic Letter
97-27; September 19, 1997
What is the Optimal Rate of Inflation?
Central banks are now placing greater emphasis on maintaining low inflation,
and this raises the question: How low should inflation be? Some say that
the current level of inflation is acceptable, while others argue that
inflation should be pushed toward zero. There are a number of ways to
think about this problem, and one approach focuses on conditions for the
optimal quantity of money. This Economic Letter summarizes the
lessons which this literature contains.
The Friedman Rule
Milton Friedman (1969) provided a simple rule for determining the optimal
rate of inflation. He started with the observation that money provides
valuable services, as it makes it easier and more convenient for consumers
to execute transactions. For example, while many establishments accept
both money and credit cards as payment for goods and services, others
accept only cash. A consumer could probably get by with credit cards alone,
but this would entail spending more time seeking out establishments that
accept them. Having some money in one's pocket saves the time and inconvenience
of doing so.
While money is useful for carrying out transactions, it is also costly
to hold. Monetary instruments generally earn less interest than securities
such as Treasury bills. In fact, some forms of money, such as currency,
earn no interest at all. The decision to hold more money means investing
less in securities that pay more interest, and the cost of holding money
depends on how much interest income is forgone. In order to decide how
much money to hold, consumers must trade off the benefits of ease and
convenience in carrying out transactions against the cost in terms of
forgone interest earnings. In the end, people strike a balance between
the two factors, holding more money when the cost is low and less when
it is high. But as long as monetary instruments pay less interest than
other securities, money will be costly to hold and consumers will have
an incentive to economize on its use.
But economizing on money is somewhat wasteful from society's point of
view. For while money is costly to hold, it is essentially costless for
central banks to produce. Thus, by increasing the quantity of real balances
(i.e., the nominal quantity of money divided by the price level), the
central bank could make everyone better off at no cost to itself. That
is, consumers would benefit from additional real balances because they
would make it more convenient to carry out transactions, and it would
cost the central bank nothing to provide this service. Robert Lucas (1987)
writes that this is "one of the few legitimate 'free lunches' economics
has discovered in 200 years of trying." Pursuing this idea to its
logical conclusion, Friedman argued that the optimal policy involves eliminating
incentives to economize on the use of money. To do so, the central bank
should seek to eliminate the difference between interest rates on monetary
instruments and on other securities, because then money would be costless
At the time Friedman wrote, money paid no interest, and the optimal
policy called for setting nominal interest rates on bonds equal to zero.
To a first approximation, the nominal interest rate equals the real interest
rate plus expected inflation. To set the nominal interest rate to zero,
it follows that the inflation rate must equal minus the real interest
rate. If the latter were around 2 to 3%, Friedman's arguments suggest
that the central bank should seek to deflate at a rate of 2 to 3%. This
would involve reducing the nominal quantity of money, but this would fall
at a slower rate than the price level, and the quantity of real balances
An alternative way to eliminate the interest differential between money
and bonds would be to pay interest on money. While monetary instruments
such as checkable deposits now earn interest, narrow measures such as
currency do not, and it is difficult to imagine a low-cost way to begin
paying interest on cash. But since currency is still essential for some
purchases, it would still be optimal for the central bank to make it costless
to hold. And since no interest is paid on currency, the Friedman rule
Seignorage and Other Taxes
Edmund Phelps (1973) criticized the Friedman rule on the grounds that
it ignores considerations related to taxation. Phelps pointed out that
inflation is a source of tax revenue for the government and that if inflation
were reduced other taxes would have to be increased in order to replace
the lost revenue. He also argued that some inflation would be desirable
if distortions associated with inflation taxes were less costly than distortions
associated with other taxes to which the government might resort.
Phelps's argument raises a number of important issues. First, in what
sense is inflation a source of tax revenue? The government can finance
its purchases in three ways: by levying direct taxes, by borrowing from
the public, and by printing money. When the government pays for goods
and services with newly printed money, it increases the money supply,
which raises the price level, and the increase in the price level diminishes
the real value of pre-existing money held by the public. Thus, inflation
works like a tax on people who hold money: the newly printed money enables
the government to buy goods and services at the expense of everyone who
held pre-exisiting money balances, which fall in real value as a consequence
of the increase in the price level. Revenue raised in this manner is called
If a central bank were to follow the Friedman rule, it would reduce
inflation and force the government to rely on other taxes to pay its bills.
Phelps argued that those taxes introduce distortions of their own, which
may outweigh the benefits of reduced inflation. What is the nature of
To a first approximation, taxes on income, consumption, capital gains,
and so on are levied on a proportional basis. Thus, for example, workers
who earn higher levels of income pay higher income taxes. This distorts
private economic decisions because it creates incentives to alter behavior
in order to avoid the tax. For example, a tax on labor income raises the
pre-tax wage that firms have to pay but lowers the after-tax wage that
workers receive. An increase in the pre-tax wage reduces the quantity
of labor that firms want to hire, and a fall in the after-tax wage reduces
the quantity of labor that workers are willing to supply. The tax makes
firms worse off because they pay higher wages but employ fewer workers
and produce less output. The tax also makes workers worse off because
they earn lower wages and work fewer hours. The government collects revenue
from the tax and uses it to provide public goods and services, but the
losses of those who pay the tax generally exceed the revenue collected.
The difference between the losses of those who pay the tax and the revenue
raised is known as the "deadweight loss" or "excess burden"
of the tax, and one principle of public finance is that taxes should be
administered in a way that minimizes these losses.
The Friedman rule would certainly not be optimal if seignorage revenue
were replaced by other tax increases that were even more distortionary.
On the other hand, the fact that governments must choose among distortionary
taxes does not necessarily invalidate the Friedman rule. The optimal mix
depends on how distortionary the various taxes are. Phelps argued that
at low rates of inflation, distortions associated with the inflation tax
might be minor and that substituting other taxes for the inflation tax
might result in greater deadweight losses. But contrary to Phelps's argument,
there are reasons to believe that the inflation tax is highly distortionary.
One is related to the fact that money is an intermediate good rather
than a final good. Intermediate goods are those goods which are used in
the production of other goods and services, and taxes on these commodities
are regarded as undesirable because they introduce two sets of distortions.
On the one hand, they reduce production efficiency and increase the cost
of producing final goods. And on the other, since this increase in cost
is reflected in final goods prices, they distort final goods markets as
well. Alternatively, the government could raise the same amount of revenue
by taxing final goods directly, and while this would still distort final
goods markets, it would not distort production efficiency.
V.V. Chari, Lawrence Christiano, and Patrick Kehoe (1996) apply this
principle to the inflation tax. They point out that money is intrinsically
useless and should not be classified as a final good. Instead, since money
is useful for facilitating transactions, it should be regarded as an intermediate
good. This line of reasoning suggests that the inflation tax is really
an indirect tax on other goods and that taxing those goods directly might
be more efficient. In fact, Chari, et al., construct a number of theoretical
examples in which this is so. In their examples, the Friedman rule remains
optimal even though seignorage revenue must be replaced by distortionary
taxes on labor income or consumption. That is, although the replacement
taxes are distortionary, their calculations suggest that the inflation
tax is even more distortionary.
Furthermore, even when the Friedman rule isn't strictly optimal, there
are two reasons why it is likely to be nearly so. First, Robert Lucas
(1994) estimates that even low rates of inflation involve substantial
welfare costs. Second, seignorage accounts for only a small fraction of
tax revenue raised in the U.S., usually less than 3%, and the adjustments
in other taxes needed to replace lost seignorage revenue are likely to
be minor. Taken together, these two facts suggest that the optimal inflation
tax is not likely to be far from the Friedman rule. For example, Casey
Mulligan and Xavier Sala-i-Martin (1997) estimate that taking replacement
taxes into account raises the optimal inflation rate by perhaps as much
as 1%. R. Anton Braun (1994) estimates that tax considerations raise the
optimal inflation rate by between 1 and 6%. Taking the average of Braun's
estimates and subtracting a real interest rate of, say, 2.5% yields an
optimal inflation rate of 1%. Thus, one can rationalize a goal of (approximate)
price stability by appealing to optimal tax arguments.
Other factors might further increase the optimal rate of inflation.
For example, the underground economy uses cash intensively and is difficult
to reach with other tax instruments. Some additional inflation might be
desirable as a tax on activity in this sector. Similarly, much of the
stock of U.S. currency is held abroad, and it might be desirable to collect
seignorage from foreigners. Quantitative information on the amount of
money held abroad or used in the underground economy is sparse, however,
and it is difficult to say how much these factors might raise the optimal
Braun, R. Anton. 1994. "How Large Is the Optimal Inflation Tax?"
Journal of Monetary Economics 34, pp. 201-214.
Chari, V.V., Lawrence J. Christiano, and Patrick J. Kehoe. 1996. "Optimality
of the Friedman Rule in Economies with Distorting Taxes." Journal
of Monetary Economics 37, pp. 203-223.
Friedman, Milton. 1969. The Optimal Quantity of Money and Other
Essays. Chicago: Aldine.
Lucas, Robert E., Jr. 1987. Models of Business Cycles. Oxford:
_____. 1994 "On the Welfare Cost of Inflation." CEPR Working
Paper No. 394.
Mulligan, Casey B., and Xavier X. Sala-i-Martin. 1997. "The Optimum
Quantity of Money: Theory and Evidence." NBER Working Paper No. 5954.
Phelps, Edmund S. 1973. "Inflation in the Theory of Public Finance."
Scandinavian Journal of Economics 75, pp. 67-82.
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