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Working P a ~ e r9113
ZERO INFLATION: TRANSITION COSTS
AND SHOE-LEATHER BENEFITS
by Charles T. Carlstrom and William T. Gavin
Charles T. Carlstrom is an economist and
William T. Gavin is an assistant vice
president and economist at the Federal Reserve
Bank of Cleveland. The authors thank David
Altig, John Carlson, Rik Hafer, and E.J.
Stevens for useful comments.
Working papers of the Federal Reserve Bank of
Cleveland are preliminary materials circulated
to stimulate discussion and critical comment.
The views stated herein are those of the
authors and not necessarily those of the
Federal Reserve Bank of Cleveland or of the
Board of Governors of the Federal Reserve
System.
October 1991
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I. Introduction
The double-digit inflation rates of the late 1970s and early 1980s were
extraordinarily high by American standards.
The costs associated with this
inflation were judged to be too high. Political recognition of these costs led
the Federal Reserve, with the support of the Carter administration, to begin
tightening monetary policy. The disinflationary policy was successful, and since
1982 the inflation rate has averaged about 4 percent. However, many have blamed
this policy for bringing about the 1981-82 recession, the worst since the Great
Depression.
Nevertheless, many would not hesitate to say that the United States is
better off today with the lower inflation rate of around 4 percent.
If the
nation is indeed better off, it is natural to ask whether a move from 4 percent
inflation to zero would be worth the costs of a possible recession. Howitt (1990)
makes a persuasive case that zero inflation is probably the best inflation rate
to inherit,but his analysis of the transition costs leaves him uncertain whether
to recommend going all the way to zero. Aiyagari (1990) compares the costs of
going to zero from a 5 percent inflation trend with the benefits of being there
and concludes that the costs exceed the benefits. In this paper, we present some
simple calculations to explain why we think that the benefits of achieving price
stability would exceed the transition costs.
One benefit of zero inflation is the value of the extra real cash balances
people wouldhold at alower inflation rate. This benefit is sometimes referred
to as the "shoe-leather"savings because, in a simple money demand model, holding
larger amounts of cash saves shoe leather that would be worn down in making
additional trips to the bank.
Because inflation acts as a tax on cash,
individuals spend time and resources (shoe leather) trying to economize on the
cash they hold. Banks benefit if inflation is zero because reserves do not earn
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interest and are therefore also taxed with inflation. Some economists consider
the shoe-leather costs so small relative to other costs of inflation that they
should not be considered by po1icymakers.l Other economists believe that the
welfare loss arising from a recession caused by tight monetary policy is so large
that it swamps all the benefits associated with zero inflation.=
In this paper, we show that the loss associated with a money-induced
recession is actually of the same order of magnitude as the gain attributable to
reduced shoe-leather costs if the inflation rate were reduced from 4 percent to
zero.
This result is important because the transition costs associated with
ending inflation are thought to be large, capturing the main cost of a
disinflation policy, while the shoe-leather costs are generally thought to be
only a small, insignificant share of the total costs of inflation.
In order to make such comparisons useful, the costs and benefits of
reducing inflation must be in the same metric. Ideally, both should be measured
in welfare terms; that is, how much a person would have to be compensated in
order to be indifferent to a given policy change. Unfortunately, this is not
possible without a consistent model that explains both how disinflationary
policies cause recessions and why people are better off with zero inflation.
Instead, we measure the desirability of a zero inflation policy in terms of
resource costs and resource savings.
We begin the analysis in section I1 by estimating the costs of a
disinflationary policy.
Then, in section I11 we show that the partial
equilibrium estimates of shoe-leather costs are equal to the value of resources
that would be saved if the price level were stable.
quantitative comparison of these offsetting effects.
with a discussion of the policy implications.
This framework allows a
In section IV, we conclude
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11. The Costs of Disinflation
For the sake of the argument, we assume that the transition to zero
inflation cannot be accomplished without causing a recession.
In theory, the
depth of the recession caused by disinflation can be reduced (or perhaps even
eliminated) if the monetary authorities can make a credible commitment to
achieving price stability. Actual losses will likely depend on the credibility
of the Federal Reserve System, making the true costnenefit calculation of a
prospective disinflation quite difficult.
In the absence of good information
about the Fed's credibility, we assume that the transition costs of another 4
percent disinflation would be the same as the costs incurred in the early 1980s
when the Federal Reserve engineered a 4 percent disinflation, reducing the
inflation trend from approximately 8 percent to 4 percent.
The transition costs are measured as the accumulated value of consumption
lost during the period from the beginning of the disinflation policy in 1979
until consumption returned to its trend level in 1985. Unlike Blinder (1990),
we use consumption rather than output to measure the costs of disinflation. We
assume that current consumption is a sufficient statistic for future output; that
is, when the level of consumption returns to its long-run trend, we assume that
the present discounted value of expected output has also returned to its long-run
trend.
This assumption is an implication of the permanent income hypothesis,
which postulates that consumption is a constant fraction of permanent income
(present discounted value of future output).
Thus, when consumption returns to
the same value that would have occurred without a recession, so has permanent
income or expected future output.
To measure the present discounted value of consumption lost because of the
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disinflation policy, one must know the path that consumption would have followed
had the policy not been adopted. We assume that the trend in consumption would
have grown at a constant rate of 2.7 percent; this is the trend growth in
potential GNP for the 1980s as calculated by the research staff at the Board of
Governors of the Federal Reserve System and as described in Braun (1990).
The expected trend in the inflation rate was around 8 percent per year in
the summer of 1979, before the Fed adopted the disinflation policy.
1983, inflation has averaged just over 4 percent per year.
Since
The recession had
ended by 1983, but consumption did not reach the level that would have occurred
without the recession until 1985 (see figure 1).
In the second half of the
decade, the level of consumption spending was above our estimate of the
sustainable long-run trend.
We estimate the costs of disinflation by
accumulating the discounted deviations of consumption below the trend level for
each year until actual consumption returned to the trend:
where X is the present value of the consumption lost, cP,
is the trend
(logarithmic) level of consumption in period t, cat is the actual logarithm of
consumption in period t, and B-l/(l+r)
is the discount rate. Assuming that the
real interest rate was 4 percent and that the consumption trend was 2.7 percent,
the present value of the consumption lost in the early 1980s was almost 18
percent of consumption, or 12 percent of the 1979 level of GNP.
Table 1 shows the sensitivity of our results to alternative assumptions
about the real interest rate and the real consumption growth trend. The results
are practically insensitive to alternative interest rate assumptions.
The
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welfare losses are shown with artificial precision, out to two decimal points,
to illustrate a difference associated with a 1/2 percentage point change in the
real rate. The assumption about the consumption growth trend, on the other hand,
is quite important for the estimate of the transition costs. In the neighborhood
of the 2.7 percent trend, each 0.1 percentage point increase in the assumed
growth trend for consumption raises the estimate of the resource cost by about
1 to 1-1/4 percent of GNP.
There are several possible objections to our procedure. First, some have
argued that the transition costs are not linear as the inflation rate is reduced.
They reason that going from 8 percent to 4 percent is credible, while going from
4 percent to zero is not.
A rationale for this argument can be found in the
reputation equilibrium model developed by Barro and Gordon (1983).
However,
there is no evidence that the disinflation in the early 1980s was anticipated.
As mentioned above, at least one forecaster, Data Resources Inc. (DRI), guessed
that inflation would average 8 percent in the 1980s. In 1978, Richard B. Hoey
began surveying decision-makersfor their 10-yearinflation outlook. The average
10-year-aheadinflation expectation peaked in October 1980 at 8.82 percent.
Second, some have suggested that high unemployment in Europe in the 1980s
is evidence that reducing inflation may have long-run effects on output.
However, this experience is recent and localized and may be due to industrial
policies or labor laws.
In a study aimed directly at this long-run issue,
Boschen and Mills (1990) find that there is no effect of monetary factors on
permanent movements in real GNP.
There are many reasons to think that this procedure will overstate the
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costs of disinflation, because the recession of the 1980s was clearly associated
with many different real shocks, including the structural adjustments in the auto
and steel industries, the deregulation in transportation and financial
industries, and the oil price shock of 1979.
It is often difficult to
disentangle real and monetary factors; however, we can use DRI's 1979 estimate
of the impact of the oil price shock to adjust our calculations.
One way to adjust for this shock is to adjust the trend consumption growth
downward.
In 1979, DRI estimated that the oil price shock would cause
consumption growth to decline by 2 percent in 1980. Consumption actually fell
0.2 percent that year; we assume the difference was due to monetary policy.
After 1980, we assume that the consumption growth rate returns to the 2.7 percent
trend and grows parallel to, but below, the trend shown in figure 1.
This
adjustment reduces the estimated resource cost of the disinflation to
approximately 9.7 percent of GNP.
Our calculation of the transition costs of disinflation differs from others
because we measure these costs in terms of lost consumption rather than in terms
of additional point-years of unemployment or in terms of lost output. A recently
published book by Blinder (1987) reports estimates of the transition costs that
appear to be much larger than ours. Blinder measures output lost indirectly.
He assumes a full-employmentrate of unemployment of 5.8 percent (the actual rate
in 1979) and calculates the cost of the disinflation as the amount by which
actual unemployment exceeds 5.8 percent for the years 1980 through 1986.
He
calculates that the disinflation resulted in 12.5 point-years of unemployment.
Using Blinder's estimate of Okun's Law, a rule of thumb relating unemployment and
output, those 12.5 point-years of unemployment are equivalent to 30 percent of
GNP .
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This procedure probably overstates the cost of disinflation in two ways.
First, the natural rate of unemployment is difficult to estimate.
The large
amount of sectoral reallocation that took place in the early 1980s makes it
likely that the natural rate was higher than 5.8 percent.
The second way Blinder overstates the cost of the 1980-1982 recession is
to add up lost output until unemployment (and, by Okun's Law, GNP) returns to its
trend level. As we discussed earlier, however, the costs of disinflation should
be measured as the accumulation of deviations of consumption from trend, and not
the accumulation of deviations of GNP from trend. Measuring lost GNP involves
a type of double counting.
The measure of accumulated output lost includes
forgone investment,which is a source of future consumption. By accumulating the
consumption lost in each year until the level of consumption returns to its
trend, we have implicitly included the investment that was lost in the
recession.
Blinder also assumes that the reduction of inflation in the early 1980s was
6 percent, not 4 percent as we have assumed. Thus, we may be overstating the
costs of a 4 percent disinflation. Assuming that inflation was reduced by 6
percentage points in the early 1980s and that the costs of disinflation are
linear, the estimated costs of reducing inflation are approximately two-thirds
of those shown in table 1.
Our calculations put the costs of the 1980s disinflation between 8 percent
and 15 percent of GNP.
Of course these calculations are only rough estimates,
but they indicate that, at least for this episode, the estimated costs of going
to 4 percent inflation were substantial.
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111. Shoe-Leather Costs
The shoe-leather benefit of eliminating inflation is the value society
places on the extra money balances that would be held if inflation were expected
to be zero. The demand for money (see figure 2) reflects the social value of an
extra unit of cash balances. If the current nominal interest rate is 8 percent
per year, society would value an additional dollar of real cash balances at eight
cents per year. This value can be considered the increased utility of holding
realbalances, as in Sidrauski (1967), or the reduced shoe-leather costs, as in
Baumol (1952) and Tobin (1956).
As is well known, the area under the demand curve for money, from the
origin to a given quantity of money, is equal to the total value per year that
society places on holding that amount of real cash balances.
The shaded area
(A+B in figure 2) is equal to the social value of the extra real balances that
would be held if the inflation rate were reduced from
.rr
to zero.
Area C in
figure 2 shows the welfare loss that remains even at zero inflation.'
This area is a partial-equilibrium measure of the welfare cost of zero
inflation. The costs of disinflation are expressed in terms of resource costs,
however, so that these benefits should also be expressed in similar terms. To
see that the traditional measure of the welfare cost of inflation also equals the
amount of resources that society wastes under positive inflation, consider a
variant of the Tobin-Baumol model of money demand.
Suppose individuals get paid once per month and choose how many times they
wish to go to the bank in that month. More trips allow the individual to hold
a lower cash balance and a higher level of interest-earning assets, such as
bonds.
With n trips to the bank per period, the average amount of an
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individual's real cash balances (m) is given by y/2n, where y is the amount of
real earnings per month. The total cost of making n trips to the bank, C(n,y),
depends on the income level, y, as well as on the number of trips to the bank,
n. Individuals choose n in order to minimize the combined costs associated with
holding currency and going to the bank:
Total Costs
=
& +C(n ,y),
(r+n)
where
a2 C(~,Y) 1 0 .
anz
The first term represents the opportunity cost of holding currency, and the
second term is the shoe-leathercosts incurred making trips to the bank in order
to minimize real cash holdings. The deadweight loss associated with an inflation
rate of n is simply the total amount of resources that are spent trying to escape
the inflation tax, c [n*(i=r+n) ,y].
The benefits of ending inflation equal the
savings in brokerage fees or shoe-leather costs, C[n*(i-r+n) ,y] - C[n*(i-r) ,y].
Appendix 1 shows that this difference is equal to area A+B in figure 2.
To derive a quantitative estimate of the benefits of going to zero
inflation, we assume that the demand for real cash balances has the general
functional form presented in Cagan (1956) and has a unitary income elasticity.
The demand for money is given as
Figure 2 shows that integrating equation (3) from m, (money demand at
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i=r+x) to m',
(money demand at i-r) gives us a framework for estimating the
resources savedby adopting a zero inflation policy.
The resource cost per year
as a fraction of current GNP, b, associated with an inflation rate of .rr (per
year) is shown in appendix 2 to be approximately
where V is base velocity in a year, i is the nominal interest rate per year, and
B is the semi-elasticity of money demand. We use the monetary base because it
is the base for the inflation tax.
Although there is a restriction against
paying interest on the business demand deposits in MI, banks have long devised
methods for paying implicit interest on these accounts. Given the structure of
financial regulations in the United States, there is probably a welfare loss
associated with inflation-induced distortions in the use of inside money.
It is
not appropriate, however, to measure the welfare loss as the area A+B under the
demand curve for inside money as illustrated in figure 2.
The income velocity of the monetary base was approximately 19 in 1990.
Assuming the real interest rate, r, to be 3.5 percent, and the semi-elasticity
of money demand to be 5, the reduction in the deadweight loss that would occur
from eliminating a 4 percent inflation rate is approximately 0.064 percent of GNP
each year.
This is seemingly a small amount, but one must remember these are only the
one-year savings.
By going to zero inflation and staying there, the savings
would also include the present discounted value of all future savings.
If the
long-run income elasticity of money demand is approximately 1.0, the benefit will
grow approximately one - for - one with the economy.
The present discounted value
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of the benefits of going to zero inflation would be b/(r-g) , where g is the
growth rate per year of output. Assuming trend growth in output is approximately
2.7 percent per year and the real interest rate is 3.5 percent per year (as
assumed in the previous section), the total benefits of a zero inflation policy
would be about 8.0 percent of current GNP.
Table 2 shows how the estimate of the welfare gain from going to zero
inflation varies with changes in assumptions about the model's parameters. The
semi-elasticity of interest, j3, varies between 3 and 7. This range encompasses
the empirical estimates of the long-run interest elasticity of the monetary base
reported in Hoffman and Rasche (1989).
The size of the welfare gain depends
importantly on the real interest rate and the real growth rate. This difference,
(r-g), is shown in the first column. We report results for three values of the
real interest rate and three values of @.
The estimate of the welfare gain
ranges from 3.1 percent to 28.6 percent of GNP.
Discussion of Assumptions
To this point our analysis ignores the fact that eliminating inflation
depletes tax revenue that must be replaced with some other distorting tax.
Phelps (1973) notes that Friedman's rule might not be optimal in a world with
distortionary taxes. He argues that the government might find it advantageous
to collect some revenue through inflation. Using our estimates of the resource
costs of inflation (equation [6]), one can calculate the additional loss that
occurs per additional dollar of revenue gained through inflation:
Evaluated at zero inflation, the loss for each additional dollar gained by
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increasing inflation is simply pr/(l-pr).
This implies that at zero inflation,
every additional dollar of revenue that the government collects via inflation
costs society an additional 25 cents in social 10~s.'~At 4 percent inflation,
the last dollar redistributed costs society more than 66 cents! If the marginal
welfare cost of raising revenue through some source is less than 25 cents, then
the inflation tax would not be part of an optimal tax structure.
Our estimates of the resource costs of inflation are overstated because we
do not include the amount of resources society must use to replace the revenue
that accrues with 4 percent inflation. Any such estimates are beyond the scope
of this paper. We proceed assuming they are negligible, but recognize that these
costs should be estimated and included in a full costbenefit analysis.
Aiyagari (1990) argues that much of the U. S. currency stock is held in the
underground economy or by foreigners and, therefore, we should not include the
full amount of the base in our resource cost estimate.''
Assuming, for example,
that two-thirds of the monetary base is held by foreigners or the underground
economy, effective velocity should be 57 instead of 19. This would reduce our
welfare costs by a third.
However, this assumes that the interest elasticity of base demand is the
same for everyone. The benefit of using currency is often the evasion of taxes
or the avoidance of punishment for breaking the law. For the inflation rates
that have historically prevailed in this country, the use of currency is likely
to be very insensitive to the interest rate. Since the measured monetary base
includes a mixture of these highly inelastic funds and the more interest-elastic
funds held for legitimate purposes by U.S. citizens, the actual interest
elasticity of base demand by aboveground holders of the monetary base must be
much larger than the level estimated using the actual measured base.
If that
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part of the monetary base held by foreigners and by the underground economy is
completely insensitive to the interest rate, then adjusting the size of the
monetary base downward to exclude this portion causes a proportional upward
adjustment in the estimated interest elasticity.
Using equation (6) with a
proportional increase in velocity and the interest elasticity leads to an
in the estimate of the benefits of price stability. The present value
of the shoe-leather savings rises from 8.0 percent to 10.3 percent of GNP for our
base case when we assume the income velocity of money is equal to 57 and the
semi-elasticity of money demand is 15.
IV. Conclusions
In summary, estimates of both the resource costs and benefits associated
with disinflation can vary widely depending on the assumptions used in the
analysis. The costs of an actual disinflation policy would range anywhere from
something quite low if policy were credible and announced in advance to a high
of around 15 percent of G N P .
A comparison of the estimates in tables 1 and 2
shows that the transition costs of a disinflation policy from 4 percent to zero
are in the same ballpark as the expected benefits of reducing shoe-leathercosts.
Our point is not to argue that these costs are identical, or even that one is
greater than the other, but merely to show that they are probably of the same
order of magnitude.
A measure of resources is not always a good measure of welfare.
The
resource costs of ending inflation are identical to the welfare costs of ending
inflation if individuals care only about consumption and if the resulting losses
are borne equally by all members of society. Clearly, the first assumption is
false. Using a model that includes both consumption and leisure in utility would
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imply that the welfare costs of ending inflation are smaller than the resource
costs. The second assumption is also clearly not true. On average, those who
become unemployed lose much more than those who keep their jobs. This would tend
to make the resource costs of eliminating inflation less than the welfare costs.
Thus, our measure of the costs of reducing inflation may either understate or
overstate the actual welfare costs.
Our measure of the resource costs of ongoing inflation is derived from a
partial equilibrium analysis.
One would prefer, however, a full general
equilibrium measure of these costs.
Gillman (1990) and Benabou (1991) , in a
discussion of Cooley and Hansen (1991), both argue that partial equilibrium
measures (the area under the money demand curve) will be less than those
estimated in a general equilibrium model with a cash-in-advanceconstraint. A
formal welfare analysis requires a general equilibrium model that can explain why
ending inflation is costly and why people prefer zero inflation.
The purpose of this paper is to show that the transition costs of ending
inflation, a major obstacle to monetary policy reform, are approximately equal
to the shoe-leather benefits of having price stability.
Summers (1991)
convincingly argues that the shoe-leather costs of inflation pale in comparison
to other costs. The most important measurable costs are those resulting from the
interaction of inflation with our nominal tax system. Indexing does not seem to
be a practical way to solve the problem.
For example, despite the indexing
provisions contained in the Economic Recovery Act of 1981, Altig and Carlstrom
(1991b) estimate that bracket creep reduces steady-state output by 1.25 percent
when the inflation trend is 4 percent. Bracket creep is the process by which
inflation pushes individuals into higher tax brackets.
If steady-state
consumption also falls by 1.25 percent, then this resource cost of inflation is
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more than 100 times larger than our estimate of the shoe-leather costs.
An even larger distortion occurs because we tax nominal interest income.
Altig and Carlstrom (1991a) estimate that this practice reduces steady-state
output by nearly 5 percent when the inflation trend is 4 percent. Again, these
costs clearly swamp both the shoe-leather costs of maintaining a 4 percent
inflation trend and the transition costs of ending inflation.
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Footnotes
1. See Summers (1991) for a recent statement of this argument.
2. See, for example, Blinder (1987), chapter 2.
3. See Data Resources, Inc. (1979), which predicts 8 percent inflation for the
next decade. The Consumer Price Index rose 7.6 percent in 1978 and 11.3 percent
in 1979.
4. See Hoey (1989) for a list of the survey results going back to 1978.
5. See Blanchard and Summers (1986).
6. For the same reason that including investment expenditures represents a form
of double counting, so will including durable goods in our measure of lost
consumption. Since we do not have a good measure of the flow of services from
durable goods, we decided to err on the side of making these costs appear larger.
7. See Bailey (1956) for an early exposition of the welfare costs associated
with inflation. A loss remains at zero inflation because, as Friedman (1969) has
argued, the optimal rate of inflation is achieved when prices fall at the real
rate of interest so that the nominal interest rate is zero. This paper does not
attempt to argue that zero, per se, is optimal.
8. This number is in line with those obtained by Fischer (1981). He estimates
that a 10 percentage point decline in inflation would produce benefits of 0.3
percent of GNP. With our formula, we also obtain savings approximately equal to
0.3 percent per year. Fischer's estimates were obtained assuming that base
demand is of the constant elasticity form, ln(m)
a + ln(y) - bln(i).
-
9. See Hallman, Porter, and Small (1991) as well as Hoffman and Rasche (1989)
for evidence that the long-run income elasticity of money demand is unity.
Hoffman and Rasche present results for the monetary base.
10. Marty (1976), using a constant elasticity form of base demand, estimated
that the additional deadweight loss per dollar of revenue gained equals ai/(ia )
Using Fischer's (1981) estimate (see footnote 1) that the elasticity of
money demand is approximately 0.25, at zero inflation societywould also lose 25
cents per extra dollar of revenue gained. See also Barro and Fischer (1976) and
McCallum (1989) for a discussion of this issue.
.
11. See Avery et al. (1987) for information about the distribution of currency
among alternative users.
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Table 1. The Resource Costs of Eliminating a 4 Percent Inflation
("transition" costs as a percent of GNP)
Real
Interest Rate
Trend Growth in Consumption
...............................
a
Consumption just returns to the 2.9% trend in 1985 and then
falls below the trend in 1986 and 1987. We assume the cost of
the disinflation is over in 1985. Consumption returns to the
2.5% trend in 1984.
Source: Authors' calculations.
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Table 2.
The Welfare Gain from Eliminating a 4 Percent Inflation
("shoe-leather" gains as a percent of GNP)
Real Interest Rate
Minus
Real Growth Rate
Source:
Semi-Interest Elasticity of Money Demand
.....................................................
Authors' calculations.
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7.55 1
1979'
I
I
I
I
I
I
I
I
1980
1981
1982
1983
1984
1985
1986
1987
Year
Source: Economlc Report 01 t h e P r e ~ l d e n t .
I
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FIGURE 2
Source:
THE WELFARE COSTS OF INFLATION
Authors.
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24
Appendix 1
From equation (I), individuals choose the number of trips to the bank, n, such
that
Solving the above equation for i and substituting m for Y/2n yields a general
form of the Baumol money demand function. The benefit of going to zero inflation
is the area under the money demand curve from m*( i-r+n) to m*( i-r) :
With a simple change of variables, this equals
which is simply the savings in shoe-leather costs associated with going from an
inflation rate of n to zero.
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25
Appendix 2
From equation (3), the benefit of going to zero inflation is
Integrating the above expression and using equation (3) yields the following
welfare gain:
Rearranging terms, we get
l + p r ~ m- xm* (i=r+x) .
B
Since the semi-elasticity of money demand with respect to the interest rate is
Constant ,
Substituting from equation (A2.5) into expression (A2.3) and defining V
-
Y/m
yields equation (5) in the text (Y enters because b is stated as a fraction of
GNP) .
@FedFRASER