significance, implying that the double-log function with constant elasticity of less than one is a more accurate characterization of the actual data.
IV. The Welfare Cost of Inflation
In the theoretical literature, it is a widely accepted idea that seigniorage is a certain amount of revenue a government collects, with the aid of its central bank, from the issue of
monetary base. Seigniorage can be viewed as a tax on private agents’ domestic currency holdings because money creation causes inflation, thereby lowering the real value of
nominal assets. Inflation imposes a tax on money holdings because it is the rate at which individuals lose the purchasing power of a dollar. Therefore, individuals change their
holdings and their use of money to lower the total cost of holding money when inflation rises. Their efforts to do so, however, reduce total services from real money balances,
thereby lowering individuals’ welfare. This loss is the welfare cost of inflation.
Table 6. Testing the Proper Specification of Money Demand Partial Adjustment Model
Wald Test Wald Test
LR Test LR Test
MoneyScale Semi-log
Double-log Semi-log
Double-log CurrencyGDP
27.703 3.7564
15.172 3.7040
CurrencyCONS 24.053
3.7765 14.238
3.7924 DepositsGDP
0.0271 0.2717
0.0130 0.2212
DepositsCONS 0.0524
0.2287 0.0040
0.1692 MBGDP
12.795 2.4522
6.2358 2.1856
MBCONS 12.338
2.5226 6.7020
2.4152 M1GDP
8.4344 0.9263
4.1316 0.8360
M1CONS 7.0691
0.8520 3.8862
0.8218
Note: This table presents the Wald and Likelihood Ratio LR test statistics for determining the correct specification of U.S. money demand estimated with the partial adjustment model. For each monetary aggregate and each scale variable, the
semi-logarithmic form is rejected but the double-log form is not at the 5 percent level of significance since the critical value is x
1,0.05
5 3.84. The semi-logarithmic form is not rejected when money is identified with demand deposits.
Table 7. Testing the Proper Specification of Money Demand Error Correction Model
Wald Test Wald Test
LR Test LR Test
MoneyScale Semi-log
Double-log Semi-log
Double-log CurrencyGDP
25.919 1.898
20.512 2.515
CurrencyCONS 21.210
2.183 18.246
3.097 DepositsGDP
12.001 0.465
7.954 0.520
DepositsCONS 5.478
1.345 3.298
1.733 MBGDP
29.016 2.302
23.151 3.596
MBCONS 22.027
2.144 18.859
3.685 M1GDP
15.168 0.419
10.428 0.456
M1CONS 9.225
0.777 6.634
0.842
Note: This table presents the Wald and Likelihood Ratio LR test statistics for determining the correct specification of U.S. money demand estimated with the error correction model. For each monetary aggregate and each scale variable, the semi-
logarithmic form is rejected but the double-log form is not at the 5 percent level of significance since the critical value is x
2,0.05
5 5.99. The semi-logarithmic form is rejected at the 10 not at the 5 level of significance when demand deposits scaled with
consumption is used as the appropriate monetary aggregate.
246 T. G. Bali
In this section, we attempt to quantify the welfare loss of deviating from a zero inflation policy and answer the question: How much welfare does the United States gain in moving
from zero inflation to the Friedman optimal deflation rate needed to bring nominal interest rates to zero? We also measure the sensitivity of the estimated welfare cost of inflation to
the specification of money demand and to the definition of money in both the currency– deposit model and the single-monetary-asset model.
We first use the quadratic approximation for the semi-log function and the square root formula for the double-log function, originally introduced by Lucas 1994 in a single-
monetary-asset model, then the consumer’s surplus approach of Bailey 1956. Bailey’s original study uses the constant semi-elasticity Cagan-type demand for money, and as will
be demonstrated in this section, the semi-log function yields a quadratic formula for the welfare loss. In this case, the welfare cost of inflation increases with the square of the
interest rate, assigning large costs to very high rates of inflation but trivial costs to moderate inflation’s. That is, with the semi-logarithmic form, the objective of a zero
inflation rate has negligible benefit, and an additional gain in moving from a zero inflation rate to a zero nominal interest rate that would attain the Friedman 1969 optimum is
assigned an even smaller value. We will also provide a square root formula for the welfare cost of inflation as an alternative to Bailey’s consumer’s surplus argument that uses the
appropriate area under a semi-log money demand function as an estimator of the welfare cost of inflation.
Lucas compares two economies with the same preferences and technology, both in a deterministic steady state with constant rates of money growth and price inflation, and
constant nominal interest rates equal to the common real rate plus the inflation rate. He assumes that in one economy monetary policy induces a steady deflation at the Friedman
optimal rate corresponding to a nominal interest rate of zero; while in the other money grows so as to induce a positive nominal interest rate. In this setting, the welfare cost of
inflation is defined as the fraction of income people would be willing to forego to move from the second economy to the first.
Following Lucas, we will now assume that each household in the model described in section II is endowed with one unit of time, which is inelastically supplied to the market
and which produces y
t
5 y 1 1 F
t
units of the consumption good in period t. Hence one equilibrium condition is c
t
5 y
t
5 y 1 1 F
t
. Now consider a balanced growth equilibrium in which the money growth rate is constant at j 5M
t11
2 M
t
M
t
, so that the inflation factor 1 1 p is constant at the value 1 1 j11F, the real currency-real
income ratio m
t
y
t
5 m
t
c
t
is constant at m , and the real deposit-real income ratio d
t
y
t
5 d
t
c
t
is constant at d. In this case, equations 7a and 7b become: u
m
~1,m ,d 5 iu
c
~1,m ,d
21a u
d
~1,m,d 5 ~i 2 i
d
u
c
~1,m ,d
21b where m
and d are the steady-state levels of currency and deposits both as a share of income, respectively. Let m
i denote the m value that satisfies equation 21a, expressed
as a function of the nominal rate of interest and d mi denote the d value that satisfies equation 21b, expressed as a function of the difference between the nominal rate of
interest and the nominal deposit rate: i 2 i
d
5 mi. The flow utility enjoyed by the
Welfare Cost of Inflation 247
household in the steady state is u 1, m i, d mi.
7
Provided that m 9i [5 m
ii] , 0 and d9mi [5 d mii] , 0, this utility is maximized over nonnegative nominal
interest rates at i 5 0: the Friedman rule of a deflation equal to the real rate of interest. We define the welfare cost wi of a nominal rate of interest i to be the percentage
income compensation needed to leave the household indifferent between i and 0. That is, wi is defined as the solution to:
u1 1 w~1,m ~i,d~mi 5 u1,m
~0,d~0. 22
Our objective is to use an estimated m i and dmi to obtain a quantitative estimate of the
function wi. One way to do this is to take the second-order Taylor series expansion of the function wi about the zero nominal interest rate. The first two derivatives of wi are
found by using equations 21a, 21b, and 22. Total differentiation of 22 gives:
u
c
w9i 1 u
m
m 9i 1 u
d
md9mi 5 0, which can be written as: w9i 5 2 u
m
u
c
m 9~i
2 u
d
u
c
md9~mi 5 2im9~i 2 im
2
d9~mi since u
m
u
c
5 i from equation 21a and u
d
u
c
5 i 2 i
d
5 mi from equation 21b. Then we find the second derivative of wi with respect to i: w0i 5 2m
9i 2 im 0i 2 m
2
[d9mi 1 imd0mi]. Thus, the Taylor series expansion of the function wi about i 5 0 gives
w~i 5 w~i u
i50
1 w9~i u
i50
~i 2 0 1 1
2 w0~i
u
i50
~i 2 0
2
5 1
2 i
2
2 m 9~0 2 m
2
d9~0 23
because wi u
i50
5 w9i u
i50
5 0 and w0i u
i50
5 2m 90 2 m
2
d90. To quantify the right side of equation 23 for the semi-log function used by Cagan 1956 and Bailey 1956,
we will use estimates of the semi-elasticity 1
m ~i
m 9~i 5
1 d~mi
d9~mi 5 2h assuming that the demand for currency and deposits have the same semi-elasticity. In terms of h,
equation 23 can be written as:
8
w~i 5 1
2 hi
2
m ~0 1 m
2
d~0 24
where m 0 and d0 are the inverses of the annual income velocities of currency and
deposits at i 5 0, respectively, assuming that i is an annual nominal interest rate and income is normalized at unity.
7
The general solution for m and d from equations 21 implies that both are functions of both interest rates
i and i
d
. But, the zero-profit condition, i
d
5 1 2 mi, under perfect competition implies that m and d are
functions of i and mi, respectively.
8
Assuming different semi-elasticities for currency and deposit demand schedules, 1
m ~i
m 9~i 5 2h for
currency and 1
d~mi d9~mi 5 2« for deposits, the welfare cost of inflation for the semi-log function in the
currency–deposit model can be written as: w~i 5
1 2
i
2
hm ~0 1 «m
2
d~0.
248 T. G. Bali
To obtain an explicit form of wi, we need an estimate of the semi-elasticity h. Here and below, we will use the parameter estimates obtained from 1957:I–1997:II quarterly
U.S. time series. We will now illustrate the procedure for finding a general formula for the semi-log function in the currency– deposit model. Assuming that the functions m
i and dmi pass through the points m
, i 5 0.0509, 0.0520 and d
, m i
5 0.1034, 0.0042 observed in 1997:II and using the constant semi-elasticity
9
h 5 7.8365 a
1
in footnote 8, we obtain the estimate m
0 5 0.0509e
7.83650.0520
5 0.0765 because m i 5 m
0 e
2hi
, and d0 5 0.1034e
7.83650.0042
5 0.1074 because dmi 5 d0 e
2hmi
. Hence, from equation 24, the estimated welfare cost of inflation evaluated at the mean
of the reserve ratio m
mean
5 0.1373 is:
10
w~i 5 ~0.301i
2
. 25
The second column of Table 8 presents some values of this quadratic function, which implies a welfare cost of a 10 percent nominal interest rate at about 0.30 percent of GDP.
Assuming the real rate of interest is around 3 percent, reduction to a 3 percent nominal rate about the rate associated with zero inflation reduces the cost to about 0.03 percent of
GDP, for a gain of about 0.27 percent of GDP. The additional gain in moving from a zero inflation to the Friedman rate is negligible 0.03 percent of GDP with the quadratic
welfare cost function given in equation 25.
In the single-monetary-asset model, the welfare cost of inflation wi is defined as the solution to: u[1 1 wi, m
i] 5 u[1, m 0] where m
i denote the m value that satisfies
u
m
1, m 5 i u
c
1, m . Following the same procedure illustrated above for the currency–
deposit model, the Taylor series expansion of the function wi about i 5 0 gives wi 5 1
2 m
0hi
2
where h represents the interest semi-elasticity of demand for M1 or the monetary base.
Using the long-run parameter estimates of the partial adjustment model
11
shown in Table 5, the quadratic approximation to the welfare cost of inflation with the semi-log
demand for M1 and for the monetary base turns out to be wi 5 0.821i
2
for M1 and wi 5 0.304i
2
for the monetary base. As demonstrated in columns 2, 4, and 6 of Table 8, the welfare cost of inflation estimated with the monetary base is found to be almost the
same as the welfare cost computed in the currency– deposit model and both of these estimates are about one-third of the welfare loss estimated with M1.
A second way to obtain the welfare cost of inflation in the currency– deposit model is to parameterize the flow utility function uc
t
, m
t
, d
t
in a particular way, estimate the parameters and calculate wi exactly. We use the CES utility function presented in
9
In the restricted case where we assume the demand for currency and deposits have the same semi-elasticity, the long-run regression coefficients, obtained from the estimated asset demand equations with the semi-log form:
log my
t
5 a 2 a
1
i
t
and log dy
t
5 a
2
2 a
1
m
t
i
t
, are found to be a 5 22.5990 29.5959, a
1
5 7.8365 1.8886 and a
2
5 22.0713 215.578 with t ratios in parentheses.
10
Following the same procedure for finding wi with different semi-elasticities of demand for currency h 5 3.693 and for deposits e 5 72.317, the estimated welfare cost evaluated at the mean of the reserve ratio
m
mean
5 0.1373 turns out to be wi 5 0.209 i
2
.
11
As presented in Table 5, the long-run parameter estimates from the partial adjustment and the error correction models are almost the same, implying that the long-run money demand estimates are not sensitive to
the choice of short-run dynamics. Therefore, the steady-state welfare cost measures calculated with the long-run parameters are not affected by the use of either partial adjustment or the error correction model estimates. We
choose to use the long-run coefficients of the partial adjustment model in our welfare cost calculations.
Welfare Cost of Inflation 249
Table 8. The Estimated Welfare Cost of Inflation Compensating Variation Approach
1 2
3 4
5 6
7 Interest
Semi-log Cur.-Dep.
Double-log Cur.-Dep.
Semi-log M1
Double-log M1
Semi-log MB
Double-log MB
i 0.301i
2
[1 2 0.0182i
0.5760 20.7362
2 1] 0.821i
2
[1 2 0.0478i
0.5546 20.8031
2 1] 0.304i
2
[1 2 0.0172i
0.5612 20.7819
2 1] 0.00
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.01 0.0030
0.0944 0.0082
0.2996 0.0031
0.1015 0.02
0.0120 0.1408
0.0328 0.4408
0.0122 0.1499
0.03 0.0271
0.1779 0.0739
0.5526 0.0273
0.1882 0.04
0.0481 0.2101
0.1314 0.6489
0.0486 0.2213
0.05 0.0752
0.2389 0.2052
0.7351 0.0760
0.2509 0.06
0.1082 0.2655
0.2956 0.8140
0.1094 0.2780
0.07 0.1473
0.2902 0.4023
0.8874 0.1489
0.3032 0.08
0.1924 0.3135
0.5254 0.9563
0.1945 0.3269
0.09 0.2435
0.3356 0.6650
1.0216 0.2461
0.3493 0.10
0.3006 0.3567
0.8210 1.0838
0.3039 0.3707
0.20 1.2026
0.5328 3.2839
1.6010 1.2154
0.5481 0.30
2.7058 0.6740
7.3888 2.0138
2.7347 0.6892
0.40 4.8102
0.7966 13.136
2.3715 4.8616
0.8111 0.50
7.5160 0.9071
20.524 2.6934
7.5963 0.9204
0.60 10.823
1.0087 29.555
2.9896 10.939
1.0207 0.70
14.731 1.1035
40.228 3.2662
14.889 1.1142
0.80 19.241
1.1930 52.542
3.5273 19.447
1.2020 0.90
24.352 1.2780
66.500 3.7755
24.612 1.2854
1.00 30.064
1.3592 82.097
4.0130 30.385
1.3649
Note: This table presents the estimated welfare cost of inflation in both the currency-deposit model and the single-monetary-asset model using Lucas’ compensating variation approach with two different functional forms semi-log, double-log and three different monetary aggregates currency-deposit, M1, and monetary base. Entries are multiplied by 100 and can thus be interpreted as
percentages.
250
T. G.
Bali
equation 8, which yields the double-log asset demand functions shown in equations 9a and 9b. With equations 9a and 9b, the equilibrium conditions 21a and 21b imply:
m ~i 5
S
m
t
c
t
D
5
S
g
2
g
1
D
i
t 2u
26a d~mi 5
S
d
t
c
t
D
5
S
g
3
g
1
D
~m
t
i
t 2u
26b The welfare cost is defined as the solution wi to u[1 1 wi, m
i, d mi] 5 u1 `, `. With the CES utility assumed in equation 8, the right side is finite provided u , 1, which
is to say, provided the elasticity of substitution between goods consumption and real currency and the elasticity of substitution between goods consumption and real deposits
are less than one. Using equations 26a, 26b, and the utility function in equation 8, we find that:
12
w~i 5
F
1 2
S
g
2
g
1
D
i
t 12u
2
S
g
3
g
1
D
m
t 12u
i
t 12u
G
u~u21
2 1. 27
The exact welfare cost of inflation wi given in equation 27 is calibrated by employing the estimated parameter values. For the double-log form with the currency– deposit
specification,
13
, u 5 0.4240 or b
1
5 0.4240 in footnote 13, g
2
g
1
5 0.0134 or e
b
5 e
24.3109
in footnote 13 and g
3
g
1
5 0.0149 or e
b
2
5 e
24.2063
in footnote 13. The implied welfare cost function evaluated at the mean of the reserve ratio m
mean
5 0.1373 is thus:
14
w~i 5 ~1 2 0.0182i
t 0.5760
20.7362
2 1. 28
The third column of Table 8 presents some values of this function, which yields a welfare cost of a 10 percent nominal interest rate at about 0.36 percent of GDP. Reduction to a
zero inflation rate or a 3 percent nominal rate reduces the cost to about 0.18 percent, for a gain of about 0.18 percent of GDP. Therefore, compared to the semi-log function, the
12
The CES utility function presented in equation 8 implies u~1,`,` 5
~g
1 1u
u~u21 12
1 s
1 2 1
s u1 1 w~i,m
~i,d~mi 5 g
1 1u
~1 1 w~i
~u21u
1 g
2 1u
m ~i
~u21u
1 g
3 1u
d~mi
~u21u u~u21
12 1
s
1 2 1
s where
m ~i 5
S
g
2
g
1
D
i
2u
and d~mi 5
S
g
3
g
1
D
~mi
2u
. Solving u[1 1 wi, m i, d mi] 5 u1, `, ` for wi yields
the exact welfare cost of inflation presented in equation 27.
13
In the restricted case where we assume the demand for currency and deposits have the same elasticity, the long-run regression coefficients, obtained from the estimated asset demand equations with the double-log form:
log my
t
5 b 2 b
1
log i
t
and log dy
t
5 b
2
2 b
1
log m
t
i
t
, are found to be b 5 24.3109 29.1084, b
1
5 0.4240 2.6511 and b
2
5 24.2063 25.0218 with t ratios in parentheses.
14
Lucas 1994 uses an estimate of the semi-elasticity h 5 7 of demand for M1 in the single-monetary- asset model obtained from 1900 to 1985 annual U.S. time series to obtain the interest elasticity u 5 hi, which
turn out be about 0.5. Then he finds the welfare cost estimate as: wi 5 1 2 0.045i
t 0.5
21
2 1 0.045i
t 0.5
, which he calls the square-root formula.
Welfare Cost of Inflation 251
double-log function yields a substantial welfare gain 0.18 percent of GDP of moving from zero inflation to the steady deflation of around 3 percent.
To determine the degree of overestimation due to the identification of money with M1, the same procedure is followed to find wi for M1, using u 5 0.4454 or b
1
5 0.4454 in Table 5 and g
2
g
1
5 0.0478 or e
b
5 e
23.0405
in Table 5. The exact welfare cost wi for M1 is therefore:
15
w~i 5 ~1 2 0.0478i
t 0.5546
20.8031
2 1. 29
The fifth column of Table 8 displays some values of this function, which gives a substantial welfare cost of 1.08 percent of GDP at the 10 percent nominal interest rate.
Reduction to a zero inflation rate reduces the cost to about 0.55 percent, for a considerable gain of about 0.53 percent of GDP.
We now present the exact welfare cost of inflation wi for the monetary base using the estimated parameter values u 5 0.4388 or b
1
5 0.4388 in Table 5 and g
2
g
1
5 0.0172 or e
b
5 e
24.0635
in Table 5. The implied welfare cost function is thus: w~i 5 ~1 2 0.0172i
t 0.5612
20.7819
2 1. 30
The last column of Table 8 demonstrates some values of this function. At the 10 percent nominal interest rate the welfare cost is about 0.37 percent of GDP. Reduction to a zero
inflation rate reduces the cost to about 0.19 percent, for a gain of about 0.18 percent of GDP. Therefore, compared to the semi-log function, the double-log function with the
monetary base implies substantial welfare gains 0.19 percent of GDP associated with moving from zero inflation to the steady deflation of around 3 percent.
As an alternative to the compensating variation approach of Lucas discussed above, we will now introduce Bailey’s consumer surplus approach to estimate the welfare cost of
inflation in the currency– deposit model using the semi-log and the double-log forms of asset demand functions. Deadweight social costs of raising revenue via seigniorage
collection can be interpreted as the lost areas under currency and deposit demand curves owing to inflation’s effect on their respective opportunity costs. This is the traditional
“shoe-leather” cost developed by Bailey 1956. With the general form of currency and deposit demand functions, the welfare cost WC is measured as the deadweight loss from
positive i in reducing currency demand,
E
i
f~ xdx 2 if~i, 31a
plus the deadweight loss from positive mi in reducing deposit demand,
15
In the single-monetary-asset model, the exact welfare cost of inflation wi is defined as the solution to: u[1 1 wi, m
i] 5 u1, `. With the following CES utility function, u~c
t
,m
t
5 g
1 1u
c
t ~u21u
1 g
2 1u
m
t ~u21u
u~u21 12
1 s
1 2 1
s , we find that:
w~i 5
F
1 2
S
g
2
g
1
D
i
t 12u
G
u~u21
2 1.
252 T. G. Bali
E
mi
g~ xdx 2 mig~mi. 31b
Hence, with the semi-logarithmic form of currency and deposit demand, the welfare cost of inflation as a fraction of GDP is defined as follows,
16
WC
Bailey semi-log
5
E
i
e
a 2a
1
x
dx 2 e
a 2a
1
i
i 1
E
mi
e
b 2b
1
x
dx 2 e
b 2b
1
mi
~mi 32a
WC
Bailey semi-log
5 e
a
a
1
~1 2 e
2a
1
i
~1 1 a
1
i 1 e
b
b
1
~1 2 e
2b
1
mi
~1 1 b
1
mi, 32b
and with the double-log form,
WC
Bailey semi-log
5
E
i
e
a
x
2a
1
dx 2 e
a
i
12a
1
1
E
mi
e
b
x
2b
1
dx 2 e
b
~mi
12b
1
33a
16
Most of the estimates displayed in Tables 3 and 4 have the Box–Cox parameter l , 0, rather than 0 , l , 1. Because one of this paper’s main messages is that accurate estimation of the welfare loss must be based
on the correct specification of money demand, the reader may think that the welfare cost function obtained from the nonlinear form of money demand should be introduced and discussed. However, there is no closed form or
numerical solution to the welfare cost of inflation when the nonlinear, Box–Cox form of money demand is employed. To see this, consider the following welfare cost function with the nonlinear specification we are using:
S
WC y
D
nonlinear
5
E
i
e
a 2a
1
S
x
l
1
21
l
1
D
dx 2 e
a 2a
1
S
i
l
1
21
l
1
D
i 1
E
mi
e
b 2b
1
S
x
l 2
21 l
2
D
dx 2 e
b 2b
1
S
~mi
l 2
21 l
2
D
~mi, which does not have an analytical solution. For a given value of i and m, this expression does not yield a
numerical solution even the estimated parameters a’s, b’s, l’s are plugged in. To see at least approximately how larger or smaller the welfare cost estimates will be when the nonlinear form is used, we plot the double-log
and nonlinear demand functions. The appropriate area under the nonlinear demand curve turns out to be almost the same as the one under the double-log function.
In addition, as described in Section IV, finding a welfare cost formula with the compensating variation approach requires a specific form for both the utility and the asset demand functions. Because there is no
analytical solution to the utility function,
u~m
t
,d
t
,c
t
5
E
mc
e
1
1n
S
a l1a
1
2l1n~ x a
1
l
2
dx 1
E
dc
e
1
1n
S
a l1a
1
2l1n~ y a
1
l
2
d y 1 v~c, which yields the Box–Cox form of currency and deposit demand functions we are using, we could not present
any empirical result on the welfare loss derived from the nonlinear specification.
Welfare Cost of Inflation 253
WC
Bailey double-log
5
S
a
1
1 2 a
1
D
e
a
i
12a
1
1
S
b
1
1 2 b
1
D
e
b
~mi
12b
1
. 33b
Our first important observation is that there is almost no difference between the magni- tudes of the welfare cost of inflation estimated in Bailey’s partial equilibrium and Lucas’s
general equilibrium frameworks.
17
In other words, we obtain the same result that for each monetary aggregate currency– deposit, monetary base, M1, the double-log function
implies sizable benefits in moving from zero inflation to the steady deflation of around 3 percent that would attain the Friedman optimum, while under semi-log demand these
benefits are trivial. The reader may wish to consult Table 9 to see the sensitivity of the estimated welfare cost of inflation to the specification of money demand and to the
17
Driffill et al. 1990 show that the two approaches—consumer’s surplus and compensating variation—are equivalent if inflation is assumed to leave real wealth and real interest rate unaffected. This assumption can be
taken to apply only to short-run costs of inflation. But, in the long-run, inflation may affect both real wealth and real rate of interest. In that case, the consumer’s surplus argument is not an exact measure of welfare change.
Driffill et al. 1990 mention that there are three reasons why inflation might be expected to have long-run effects on the real rate of interest and real income or wealth. First, as Tobin 1955, 1965 noted, higher inflation in
reducing the demand for real money balances may cause a switch in the portfolio of assets held in the economy; in particular, lower real money balances may cause an increase in holdings of physical capital, and this would
raise output per capita and reduce the real interest rate. This is the “Tobin” effect. Second, as Feldstein 1976 noted, in addition to these portfolio effects there may be savings effects if the saving rate depends on the real
rate of interest as would be suggested by life-cycle models of savings. Finally, depending on assumptions about the structure of taxation, higher inflation rates will have implications for the government budget constraint and
these offsetting fiscal policies may have further effects.
Table 9. The Estimated Welfare Cost of Inflation Consumer’s Surplus Approach
Interest Rate Semi-log
Currency–Deposit Double-log
Currency–Deposit Semi-log
M1 Double-log
M1 Semi-log
MB Double-log
MB 0.00
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.01 0.0029
0.0943 0.0091
0.2986 0.0031
0.1014 0.02
0.0109 0.1406
0.0348 0.4386
0.0119 0.1496
0.03 0.0233
0.1775 0.0747
0.5492 0.0256
0.1878 0.04
0.0394 0.2095
0.1266 0.6442
0.0434 0.2207
0.05 0.0586
0.2383 0.1887
0.7290 0.0648
0.2502 0.06
0.0804 0.2646
0.2594 0.8066
0.0892 0.2771
0.07 0.1042
0.2892 0.3370
0.8786 0.1160
0.3022 0.08
0.1298 0.3123
0.4203 0.9461
0.1449 0.3257
0.09 0.1566
0.3343 0.5081
1.0100 0.1753
0.3479 0.10
0.1845 0.3552
0.5994 1.0708
0.2071 0.3691
0.20 0.4730
0.5294 1.5480
1.5727 0.5406
0.5447 0.30
0.7136 0.6687
2.3253 1.9693
0.8193 0.6838
0.40 0.8905
0.7892 2.8553
2.3099 1.0132
0.8037 0.50
1.0200 0.8975
3.1861 2.6142
1.1366 0.9109
0.60 1.1203
0.9968 3.3821
2.8924 1.2112
1.0090 0.70
1.2040 1.0894
3.4943 3.1506
1.2548 1.1002
0.80 1.2787
1.1764 3.5570
3.3927 1.2796
1.1858 0.90
1.3485 1.2590
3.5914 3.6218
1.2935 1.2668
1.00 1.4154
1.3378 3.6100
3.8397 1.3012
1.3440
Note: This table presents the estimated welfare cost of inflation in both the currency-deposit and the single-monetary-asset models using Bailey’s consumer’s surplus approach with two different functional forms semi-log, double-log and three
different monetary aggregates currency-deposit, M1, and monetary base. Entries are multiplied by 100 and can thus be interpreted as percentages.
254 T. G. Bali
definition of money with Bailey’s approach. Second, the welfare cost measures in the currency– deposit model turn out to be almost the same as those in the single-monetary-
asset model when the monetary base is identified as the relevant definition of money. Defining M1 without modeling the distinctive roles of currency and deposits as the
appropriate money overestimates the true welfare cost of inflation in both the consumer’s surplus and compensating variation approaches.
The above welfare cost analysis in the currency– deposit model does not account for the significant magnitude of U.S. currency held overseas, which shifts a sizable part of the
welfare cost abroad. Because a considerable fraction of U.S. currency is held abroad, the welfare cost estimates based on currency in the paper overstates the actual cost of
inflation. How much U.S. currency is abroad is important for welfare cost estimates although currency movements are extremely difficult to measure, and estimates of the
foreign component of currency stocks and flows are subject to a great deal of speculation and uncertainty. Porter and Judson 1996 have examined ten methods for estimating the
amount of currency held abroad.
18
In their summary of all estimation methods, they derive an extreme range of 49 percent to 71 percent for the foreign share of currency and then
they say neither endpoint is likely to be correct, whereas a value near the middle, which is 60 percent, is much more likely to be so. Thus, I use the midpoint 60 percent as a
rough measure of the percentage of U.S. currency held abroad and re-estimate the welfare loss in the currency– deposit model. The corrected welfare cost estimates are presented in
Table 10.
V. Conclusions
