Bharat Trehan

Carl Walsh

English

Research Papers in Economics

FRBSF WEEKLY LETTER
August 4, 1989
Optimal Inflation
Rates of inflation have varied widely across
countries andover time. Although economists
generally agree that sustained inflation is caused
by excessive money growth, this diversity in in-
flation experiences has led many to wonder what
factors induce a country's monetary authority to
allow excessive money creation in the first place.
As we discussed in an earlier Letter (July 21,
1989), one line of research has focused on ways
in which large fiscal deficits could force the
monetary authority to print more money and
thereby generate inflation. Another, more recent
line of research suggests that prevailing rates of
inflation, as well as prevailing tax rates and fiscal
deficits (or surpluses), taken together, may be the
government's optimal response to the need to
balance its budget over time. In this Letter, we
survey the work that has been done on the "opti-
mal inflation" issue, and discuss some relevant
empirical evidence.
What is "optimal?"
Economists use the term "optimal inflation" to
describe the inflation rate that minimizes dis-
tortions that might prevent an economy's scarce
resources from being used efficiently. Distortions
will arise when the private cost of consuming a
good and the social cost of producing it are not
equal. In this case, the "optimal" amount of
that good will not be produced and consumed. A
private cost below the social cost will lead to too
much of the good being produced, while a pri-
vate cost above the social cost will lead to too
little being produced.
To determine the optimal rate of inflation, Nobel-
laureate Milton Friedman applied this notion of
private and social costs to money. Money pro-
vides certain services of value to individuals,
such as facilitating transactions. Since money
does not earn interest, the cost of holding it
essentially is the interest income on other assets
that must be sacrificed. Because of this cost,
individuals will attempt to economize on their
money holdings. Yet the social cost of printing
more money is essentially zero. As a result, too
little money will be held, thereby introducing
economic distortions associated with higher-
than-optimal transactions costs.
In order to get around this problem, Friedman
suggested that deflation actually would be opti-
mal. Specifically, he suggested that the optimal
rate of deflation would be the rate of return on
nonmonetary assets. With prices falling aUhis
rate, non-interest-bearing money would yield a
rate of return, adjusted for price changes, equal
to that on other assets, and the opportunity cost
of holding non-interest-bearing money would be
zero-the same as the social cost of producing
money. Individuals then would be indifferent be-
tween money and other assets on a rate of return
basis, and would therefore hold enough money to
ensure that no distortions arise from insufficient
liquidity in the economy.
Revenue constraint
Deflation, however, may not be optimal because
the government faces a revenue constraint. The
government must raise revenues, by raising taxes
and/or by printing money. It is well known that
the government can use the money it prints to
purchase real goods and services, and in this
sense, inflation can be a source of revenue. If,
however, the monetary authority were to engineer
a steady deflation by retiring money, it would
have to transfer real resources to the private
sector and obtain revenues to do so from other
tax sources.
Unfortunately, obtaining increased revenues
from other forms of taxation generally will cause
distortions in economic activity, as individuals
modify their behavior in order to avoid these new
demands. Raising income tax rates, for example,
reduces the amount of consumption goods that
can be obtained for a given amount of labor, and
causes individuals to alter their decisions regard-
ing how much to work. In addition, the historical
evidence suggests that as tax rates increase,
society begins to divert increasing amounts of
resources to tax avoidance. Since these resources
are not being used for any intrinsically useful
purposes, they are a net loss to society. TheseFRBSF
losses are commonly referred to as the dead-
weight costs of taxation.
Thus, Friedman's rule eliminates distortions
arising from holding an inappropriate amount of .
money only at the cost of imposing significant
distortions on other kinds of economic decisions.
Instead, the optimal rate ofinflation is that
which, together with the taxes the governrnent
imposes, generates sufficient revenues while
minimizing distortions from bothsources.
To minimize the distortionarycosts of raising a
fixed amount of revenue atanypointintime, the
government sho.uld equate rnarginaldistortionary
costs across. all available revenue-raising instru-
ments. This means that ifthe government had
only two kinds of revenue sources available to
it, say, an income tax and a wealth tax, and the
marginill distortionary costs associated with the
income tax exceeded those associated withthe
wealth tax, thegovernmentshould lowerthe
income tax rate and raise the wealth tax rate (to
produce the same amount of totaLrevenuel until
the deadweight losses arising from the two kinds
of taxes were equalized on the margin.
Economists Milrtin Bailey and Edmund Phelps
appliedthis reasoning to the optimal inflation
question. They showed that the optimal tax pol-
icy wo.uld involve. raising revenues both from
conventional fiscal taxes and from taxing money
holdings through inflation.
Optimizing overtime
Robert Barro extended this analysis .to show that
the same principles could be used tode~ermine
the evolution of tax rates over time, assuming~
for simplicity~that inflation was not used to
raise revenues. He reasonedthat governments
would be interested in minimizing the distortion-
ary costs of taxation, not just at any pointin time,
but in the future, as well. Accordingly, they
would set tax rates. s.o thiltthe marginal distor-
tionary costs ofraisingrevenues were equal
across timeperiods. Once again, iUs easy to see
why this is an optimill policy. If thedistortionary
costs areunequal.across different time periods,
the government simply lowers taxes in. the high
distortion period qnd raises them in the low
distortion period insucha way that it obtains
the same revenue as before. The result of this
process is areduction in totaldistortionary costs
with no change in the revenue obtained over
time by the government.
Several interesting implications follow fromthis
theory. If marginal distortionary costs are pro-
portional to tax rates, the condition that the
government equate marginal costs across time
periods implies that planned tax rates be equal
across time periods as well. Thus, if.government
expenditures are perfectly predictable, tax rates
will be constant over time. Because tax rates are
never expected to change, this theory is often
called the "tax smoothing" hypothesis. Tax rates
would changeonly because of unpredictable
changes in government spending. Further, tem-
porary but predictable changes in government
spending would lead to variations in the fiscal
deficit, not changes in tax rates. The government
would run deficits during periods when spending
is above its permanent levels, and surpluses
when spending is below permanent levels.
Economist Gregory Mankiw combined Barro's
analysis with that of Bailey and Phelps to note
that if both fiscal and monetary policy are used
optimally to finance a change in government
expenditures, deadweight losses can be mini-
mized by adjusting all revenue instruments a
small amount, rather than by making a major
adjustment In one instrument. Consequently,
shocks to the government's revenue needs would
require that both tax rates and inflation be ad-
justed in the same direction. The experience of
the 1980s superficially seems consistent with
this hypothesis; tax cuts in the early 1980s were
accompanied by a major reduction in the level
of inflation.
However, tax rates can be adjusted for reasons
other than changes in permanent expenditures.
Changes in the economy's structure that affect
the relative distortionary costs of alternative
revenue sources will lead the government to
adjust itstax mix. For example, an increase in
the stock of money that the public is willing to
hold would increase the tax base against which
the inflation tax can be levied, and would
increase the revenue obtained from a given in-
crease in inflation. The optimal policy response
then is to increase inflation and lower other
taxes. In this case, inflation would move in the
opposite direction from other tax rates. Conse-
quently, in attempting to verify this hypothesis,we must be careful to identify the kinds of dis-
turbances that are the cause of changes in tax
rates and inflation.
Empirical evidence
The chart shows the behavior of the tax rate and
the rate of inflation since 1914, the year that the
Federal Reserve was founded. We measure the
tax rate as the ratio of government receipts to
GNP and the inflation rate as the change in the
GNP deflator. The chart reveals that while the
inflation rate has tended to move up and down
over time, changes in the tax rate have been
more permanent in nature. These characteristics
are especially noticeable in the period around
the two World Wars. In both cases, the rate of
inflation went up sharply, and then declined. In
contrast, the tax rate has not declined signifi-
cantly in the period following World War II.
U.S. Tax Rates
and Inflation
Percent
30
relative distortionary costs. Formal statistical
tests that control for such a possibiIity can be
used to test the tax smoothing hypothesis. One of
the implications of the hypothesis is that perma-
nent changes in the tax rate should be related to
permanent changes in inflation. However, in our
tests we find no evidence of such a relationship.
While there is some evidence of a positive
relationship between taxes and inflation in the
postwar period, this relationship appears to be
limited to short-run movements in the two series.
Other researchers have looked at data for Euro-
pean countries and have not found any evidence
that supports the tax and inflation smoothing
hypothesis. Accordingly, it appears reasonable to
conclude that the positive relationship between
taxes and inflation observed over the postwar
period in the u.s. is due to other factors. One
such factor is the well-known "bracket creep"
phenomenon: since tax rates were not indexed to
inflation over this period, rising inflation was
accompanied by higher taxes.
,........TTT"f'~ .........~..,......,.,.,...,~......,..~"TfTT"~T"""'"""T~orrl-20
1914 1922 1930 1938 1946 1954 1962 1970 1978 1986
Of course, the divergence of tax rates and
inflation could have been due to changes in
The positive response of both tax rates and
inflation to the need for greater revenue during
wartime is consistent with the tax smoothing
hypothesis. However, the hypothesis also pre-
dicts that both should have moved together after
the wars, remaining at higher levels than before
in order to payoff the debt acquired over this
period. The behavior of tax rates and inflation
in the postwar periods clearly contradicts the
hypothesis. Carl Walsh
Visiting Scholar FRBSF
and Associate Professor
University of California, Santa Cruz
Bharat Trehan
Senior Economist
Better understanding needed
The tax smoothing hypothesis is appealing
because it is based on the presumption that
prevailing levels of both tax rates and inflation
are the optimal response of policymakers to the
government's need for revenue in the presence of
distortionary costs. In this sense, the approach
attempts to find a fundamental explanation for
inflation that avoids the temptation to resort to
ad hoc factors such as oil price changes or food
price fluctuations. Unfortunately, the hypothesis
appears inconsistent with the u.s. and European
experiences. Nonetheless, prevailing levels of
inflation may still be the outcome of optimizing
behavior on the part of policymakers; our evi-
dence suggests that to explain inflation, we also
need to understand why governments often re-
sort to inflation to finance temporary bulges in
expenditures.
20
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Optimal inflation

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Optimal inflation

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