The monetary model developed in this section is quite new in the sense that it yields a specific estimable form for asset demand functions as in equations 9a and 9b, which
are used to derive the welfare cost function in a currency– deposit framework for both the consumer surplus and the compensating variation approaches. In addition, the currency–
deposit model is more general than the earlier monetary models because, as discussed in the previous section, it nests the currency-only and deposits-only models.
As presented above, standard utility functions yield double-log demands for money although the semi-log form has been widely used in money demand studies, more a matter
of convenience than theoretical or empirical attractiveness. The convenience comes from its simplicity, the fact that steady-state seigniorage is easily defined at a constant nominal
interest rate and the fact that the seigniorage-maximizing interest rate as well as the maximum seigniorage are easily derived. However, the semi-logarithmic form has its
drawbacks. The micro-foundation of the semi-log specification in either “the shopping time” or “the money-in-the-utility function” approach is somewhat ad hoc. We have to
impose a specific form on the utility function or on the shopping time technology in order to arrive at the constant semi-elasticity Cagan-type demand for money. The utility
function and the similarly shaped shopping time technology take the following unusual forms, respectively:
u~c
t
,m
t
,d
t
5 m
t
~1 1 w 2 ln m
t
a 1
d
t
~1 1 v 2 ln d
t
b 1 v~c
t
, u
m
. 0,u
d
. 0,u
c
. 0 c~c
t
,m
t
,d
t
5 m
t
~ln m
t
2 w 2 1
t
a 1
d
t
~ln d
t
2 v 2 1
t
b 1 v~c
t
, c
m
, 0,c
d
, 0,c
c
. 0 which imply the following Cagan-type demand for currency and deposits:
ln m
t
5 w 2 av
c
i
t
, ln d
t
5 v 2 bv
c
~i
t
2 i
d
~t, where the marginal utility of consumption is assumed to be a positive constant, v
c
. 0.
III. The Specification of the Money Demand Function
This section concentrates on the econometric approach we use to identify the proper specification of U.S. money demand. A search for an improved specification of the
long-run demand for money leads us to consider econometric issues in the treatment of short-run dynamics. The calculation of the parameters of long-run relationships from
estimated models, and the forms of particular models, such as partial adjustment and error correction models, are also discussed in this section.
To determine what form the U.S. money demand will take, the Box–Cox transforma- tion,
g
~l
~i
t
5 i
t l
2 1 l
, 10
Welfare Cost of Inflation 239
is applied to the i
t
variable. Note that in the following regression equation, which assumes a unitary quantity elasticity of money demand,
ln~m
t
q
t d
5 b
1 b
1
S
i
t l
2 1 l
D
1 e
t
, 11
when l equals one, equation 11 reduces to ln~m
t
q
t d
5 ~ b
2 b
1
1 b
1
i
t
1 e
t
, 12
and the demand for real money balances becomes semi-logarithmic in i
t
. When l equals zero, the transformation is, by L’Hopital’s rule,
lim
l30
S
i
t l
2 1 l
D
5 ln i
t
Hence, l 5 0 in g
l
i
t
implies that the demand for real balances is logarithmic in i
t
, ln~m
t
q
t d
5 b
1 b
1
ln i
t
1 e
t
. 13
In estimating the regression equation of the demand for real balances, the crucial step is to define the specific form of money demand and to find an efficient mechanism to
estimate short-run money demand equations, which are consistent with imposed long-run relationships. The partial adjustment and error correction models have been widely used
as short-run dynamic specification to estimate long-run parameters of money demand. In this paper, dynamics are first allowed for by means of real partial adjustment model along
the lines of Hwang 1985, who rationalizes partial stock adjustment as an optimization between costs of adjustment of money balances and costs of being out of equilibrium:
3
ln m
t
2 ln m
t21
5 f~ln m
t d
2 ln m
t21
. 14
Substituting equation 12 into equation 14 yields ln ~m
t
q
t d
5 ~ fb
1 ~fb
1
S
i
t l
2 1 l
D
1 ~1 2 fln ~m
t21
q
t21
1 «
t
. 15
As an alternative to the partial adjustment model, a general distributed lag model and its transformation to error correction have been increasingly used for estimation of money
demand. Following Baba et al. 1992 and Banerjee at al. 1993 among many others,
4
we apply the error correction mechanism to U.S. money demand. To illustrate the derivation
3
Partial adjustment is typically motivated by cost-minimizing behavior wherein the costs of disequilibrium are balanced against adjustment costs. Following Hwang 1985, consider a quadratic cost function of the form:
C 5 Ã
1
ln M
t d
2 ln M
t
]
2
1 Ã
2
[ln M
t
2 ln M
t21
2 zln P
t
2 ln P
t21
]
2
where the first and second terms of the function correspond to the disequilibrium and adjustment costs, respectively. Minimizing costs with respect to M
t
yields: ln M
t
2 ln M
t21
5 fln M
t d
2 ln M
t21
1 z1 2 fln P
t
2 ln P
t21
where f 5 Ã
1
Ã
1
1 Ã
2
. Thus, when z 5 1, this expression reduces to the real partial adjustment model in which real balances are adjusted: ln m
t
2 ln m
t21
5 f ln m
t d
2 ln m
t21
.
4
For example, Hendry 1980 used this procedure for U.K. money demand and Rose 1985 estimated an error correction model for U.S. money demand.
240 T. G. Bali
of this model from a distributed lag model, we consider a specification with only one lag of each variable as in
ln ~mq
t
5 a
1 a
1
i
t
1 a
2
i
t21
1 a
3
ln ~mq
t21
1 e
t
16 for the semi-log form with unitary quantity elasticity. Note that the long-run interest rate
semi-elasticity in this model is a
1
1 a
2
1 2 a
3
. Now subtract ln mq
t21
from both sides of equation 16 and then add and subtract a
1
i
t21
on the right hand side to get Dln ~mq
t
5 a
1 a
1
Di
t
1 ~ a
1
1 a
2
i
t21
1 ~ a
3
2 1ln ~mq
t21
1 e
t
. 17
To estimate the error correction model, equation 17 can be rewritten as Dln ~mq
t
5 a
1 a
1
Di
t
1 ~ a
3
2 1ln ~mq
t21
2 ki
t21
1 e
t
, 18
where k 5 a
1
1 a
2
a
3
2 1. Equation 18 is called an error correction model because the term [ln mq
t21
2 k i
t21
] represents last period’s error or deviation of money from its long-run relationship with interest rate.
To determine whether the money demand function with the error correction mechanism is logarithmic or semi-logarithmic, the Box–Cox transformation is applied to i
t
and i
t-1
in equation 16:
ln ~mq
t
5 a
1 a
1
S
i
t l
1
2 1 l
1
D
1 a
2
S
i
t21 l
2
2 1 l
2
D
1 a
3
ln ~mq
t21
1 e
t
. 19
Note that when l
1
5 l
2
5 0, equation 19 reduces to the error correction model with double-log function
Dln ~mq
t
5 a
1 a
1
Dln i
t
1 ~ a
3
2 1ln ~mq
t21
2 kln i
t21
1 e
t
. 20
When l
1
5 l
2
5 1, the demand for real balances takes the semi-logarithmic form given in equation 18.
Having provided the framework we utilize to identify the true form of U.S. money demand, we now describe the data, and then present the money demand estimates and
econometric test results. After all variables used in our analysis are seasonally adjusted by the standard U.S.
Bureau of Census methods of seasonal adjustment, the demand for real balances is estimated with four different monetary aggregates currency, demand deposits, monetary
base, M1, using quarterly data for the period 1957:I–1997:II.
5
Furthermore, to test whether the empirical results depend on the choice of a scale variable, two different
quantity variables consumption, income are utilized in money demand estimates. We use the GDP deflator when real GDP and the consumer price index CPI when real
consumption is employed as the scale variable. The 3-month T-bill rate is used as the opportunity cost of holding money in our estimation.
The demand for real balances is estimated by means of OLS when the short-run partial adjustment specification takes either the semi-log form: ln mq
t
5 b 1 b
1
i
t
1 b
3
ln mq
t21
, or the double-log form: ln mq
t
5 b 1 b
1
ln i
t
1 b
3
ln mq
t21
. The OLS estimates and related statistics of the partial adjustment model are presented in Table 1.
When dynamics are allowed for by means of autoregressive distributed lag model, OLS
5
Data source is International Monetary Fund International Financial Statistics on CD-ROM.
Welfare Cost of Inflation 241
is applied both to the error correction model with the semi-log function: Dln mq
t
5 a 1 a
1
Di
t
1 a
1
1 a
2
i
t21
1 a
3
2 1 ln mq
t21
1 e
t
, and the model with the double-log function: Dln mq
t
5 a 1 a
1
Dln i
t
1 a
1
1 a
2
ln i
t21
1a
3
21 ln mq
t21
1 e
t
. Table 2 shows the short-run estimates and related statistics of the error correction model. The
nonlinear money demand estimates with the partial adjustment and error correction models are demonstrated in Tables 3 and 4, respectively.
6
The long-run values of the
6
Although they are not presented in our tables, the statistical results from the augmented Dickey–Fuller 1979 test imply that all of the variables used in this study are characterized as nonstationary I1 variables
because we find that there is a unit root in the level of the variables but there is none in their first differences. Because the variables are found to be nonstationary I1, we check for cointegration using Engle–Granger 1987
Table 1. Short-Run Money Demand Estimates
MoneyScale Specification
b
0,s
b
1,s
b
2,s
R
2
Log- likelihood
h statistic ARCH1
CurrencyGDP Semi-log
20.4554 24.0831
0.5852 3.6610
0.8415 22.034
0.8963 301.8255 21.3580 0.0418
CurrencyGDP Double-log
20.8338 25.5171
0.0515 5.1047
0.7793 19.084
0.9034 307.5597 21.5507 0.1479
CurrencyCONS Semi-log 20.3070
23.7611 0.4927
3.4532 0.8730
26.545 0.9100 307.8868 22.2179
0.1426 CurrencyCONS Double-log
20.5878 25.1993
0.0430 4.8286
0.8256 23.740
0.9157 313.1096 22.5618 0.4442
DepositsGDP Semi-log
20.0281 22.0103
1.2119 2.2296
0.9832 130.37
0.9914 365.1336 22.3997 1.0901
DepositsGDP Double-log
20.0812 22.9543
0.0091 2.1818
0.9841 131.88
0.9914 365.0295 22.4957 1.2193
DepositsCONS Semi-log
20.0142 21.4230
1.1982 2.3150
0.9880 147.67
0.9931 370.2916 23.8533 6.2435
DepositsCONS Double-log
20.0675 22.9161
0.0091 2.2785
0.9889 148.93
0.9931 370.2090 23.9499 6.5574
MBGDP Semi-log
20.0750 22.6830
0.2225 2.5222
0.9685 84.818
0.9877 376.4112 0.1634
0.0240 MBGDP
Double-log 20.1700
23.6215 0.0184
3.2480 0.9582
77.349 0.9880 378.4363 20.0202
0.0446 MBCONS
Semi-log 20.0429
22.3766 0.1955
2.6021 0.9773
109.56 0.9915 391.9322 21.0842
0.0249 MBCONS
Double-log 20.1167
23.6370 0.0157
3.3492 0.9702
102.76 0.9917 394.0756 21.3411
0.0343 M1GDP
Semi-log 20.0437
23.1077 0.2385
2.7749 0.9672
94.084 0.9903 383.2190 21.9808
0.0864 M1GDP
Double-log 20.1272
23.9127 0.0186
3.3357 0.9582
84.700 0.9905 384.8668 22.1844
0.0985 M1CONS
Semi-log 20.0209
22.5054 0.2068
2.7013 0.9760
115.16 0.9926 391.7311 23.7070
0.4429 M1CONS
Double-log 20.0864
23.7658 0.0157
3.2363 0.9698
106.63 0.9927 393.2633 23.9471
0.6125
Note: This table presents the short run estimates of the demand for currency, deposits, monetary base MB, and M1 using quarterly data for the period 1957:I and 1997:II. The scale elasticity of money demand is assumed to be unity. b’s are the
coefficients in the semi-log and double-log form of money demand with the partial adjustment model. t-ratios are shown in parentheses. indicate the cases in which the h statistics and ARCH1-statistics are significant at the 5 percent 1 percent
level of significance. The short-run parameters are estimated from the following semi-log and double-log specification with the partial adjustment model: ln mq
t
5 b
0,s
2 b
1,s
i
t
1 b
2,s
ln mq
t21
semi-log, ln mq
t
5 b
0,s
2 b
1,s
ln i
t
1 b
2,s
ln mq
t21
double-log.
242 T. G. Bali
parameters presented in Table 5 are unscrambled from the short-run estimates given in Tables 1 and 2.
As pointed out earlier, this section attempts to identify the correct specification of the U.S. money demand function employing the nonlinear form of money demand with
test. According to the cointegration test results, the U.S. time series are cointegrated of order 1,1. We test autocorrelation using the Durbin-h statistics. As presented in Tables 1 through 4, there is autocorrelation in some
of the estimated money demand equations when consumption is used as the scale variable. Given the presence of a lagged endogenous variable, autocorrelation implies that OLS estimates are biased and inconsistent. We test
for the presence of autoregressive conditional heteroscedasticity using ARCH-LM test. As shown in Tables 1 through 4, there are no ARCH errors in the estimated money demand equations except for the deposit demand
scaled with consumption at the 1 percent level of significance.
Table 2. Short-Run Money Demand Estimates Error Correction Model
MoneyScale Specification
a
0,s
a
1,s
a
2,s
a
3,s
Log- likelihood h statistics ARCH1
CurrencyGDP Semi-log
20.4041 23.5375
21.1772 23.2591
20.5003 23.0255
20.1403 23.5798
303.5142 21.2971 0.0307
CurrencyGDP Double-log
20.6512 24.1221
20.1084 25.2806
20.0395 23.7465
20.1732 24.0778
312.5122 21.5923 0.5645
CurrencyCONS Semi-log 20.2807
23.3488 20.9146
22.6234 20.4394
22.9715 20.1159
23.4240 308.7831 22.1852
0.1335 CurrencyCONS Double-log
20.4806 24.0428
20.0888 24.4334
20.0349 23.7392
20.1430 23.9344
316.3572 22.5021 1.0175
DepositsGDP Semi-log
20.0234 21.8366
28.2502 26.3031
20.5717 21.1280
20.0116 21.6765
380.8015 22.3568 2.4222
DepositsGDP Double-log
20.0478 21.9185
20.0814 26.9983
20.0044 21.1690
20.0105 21.5717
384.5181 22.5171 2.7280
DepositsCONS Semi-log 20.0131
21.4162 27.5303
25.8482 20.6577
21.3450 20.0082
21.3254 383.5258 23.7762 4.8271
DepositsCONS Double-log 20.0439
22.0256 20.0697
25.9836 20.0054
21.4503 20.0074
21.2092 384.3083 24.1104 5.6003
MBGDP Semi-log
20.0620 22.2218
20.7543 23.3594
20.1683 21.8860
20.0256 22.2323
379.7219 0.2155
0.0380 MBGDP
Double-log 20.1114
22.4432 20.0741
25.8149 20.0113
22.0618 20.0279
22.3349 389.4991 20.0199
0.0398 MBCONS
Semi-log 20.0381
22.0960 20.5352
22.6000 20.1657
22.1663 20.0198
22.1949 393.5241 21.2395
0.0335 MBCONS
Double-log 20.0869
22.7340 20.0572
24.8292 20.0115
22.4697 20.0222
22.3930 401.1110 21.1174
0.0162 M1GDP
Semi-log 20.0329
22.4563 21.1330
25.5141 20.1412
21.6966 20.0228
22.3033 393.9576 21.9777
0.0038 M1GDP
Double-log 20.0792
22.5457 20.0782
26.5021 20.0106
21.9833 20.0270
22.5167 398.9437 22.2589
0.5797 M1CONS
Semi-log 20.0174
22.1534 20.9156
24.5998 20.1405
21.8620 20.0178
22.1481 398.9261 23.9091 1.1371
M1CONS Double-log
20.0617 22.7285
20.0613 25.1930
20.0107 22.2455
20.0218 22.4533
401.8222 24.0113 1.7890
Note: This table presents the short run estimates of the demand for currency, deposits, monetary base MB, and M1 using quarterly data for the period 1957:I and 1997:II. The scale elasticity of money demand is assumed to be unity. a’s are the
coefficients in the semi-log and double-log form of money demand with the error correction model. t-ratios are shown in parentheses. indicate the cases in which the h statistics and ARCH1-statistics are significant at the 5 percent 1 percent
level of significance. The short-run parameters are estimated from the following semi-log and double-log specification with the error correction model: D ln m
t
5 a
0,s
1 a
1,s
D i
t
1 a
2,s
i
t21
1 a
3,s
ln m
t21
semi-log, D ln m
t
5 a
0,s
1 a
1,s
D ln i
t
1 a
2,s
ln i
t21
1 a
3,s
ln m
t21
double-log.
Welfare Cost of Inflation 243
Table 3. Short-Run Nonlinear Money Demand Estimates Partial Adjustment Model
MoneyScale b
0,s
b
1,s
b
2,s
l R
2
Log- likelihood
h statistic ARCH1
CurrencyGDP 20.7677
25.2915 0.0088
0.9849 0.7751
19.071 20.5829
21.9382 0.9056
309.4117 22.3583
0.7421 CurrencyCONS
20.5300 24.9265
0.0059 0.8753
0.8209 23.683
20.6563 21.9473
0.9177 315.0058
23.4274 1.5833
DepositsGDP 20.5289
20.2047 0.3826
0.1431 0.9834
129.23 0.7530
0.5173 0.9914
365.1401 22.4229
1.1326 DepositsCONS
20.5574 20.2012
0.4281 0.1460
0.9882 145.84
0.6762 0.5477
0.9931 370.2936
23.8840 6.4233
MBGDP 20.1437
23.3754 0.0017
0.5878 0.9558
76.391 20.7787
21.5660 0.9882
379.5291 20.4423
0.0001 MBCONS
20.0917 23.2126
0.0013 0.5634
0.9685 101.86
20.8253 21.5921
0.9919 395.2832
21.8117 0.0044
M1GDP 20.1040
23.1641 0.0042
0.5972 0.9567
83.493 20.4956
20.9638 0.9906
385.2848 22.3844
0.0029 M1CONS
20.0650 22.6745
0.0032 0.5334
0.9688 105.42
20.5318 20.9244
0.9927 393.6742
24.1407 1.2538
Note: This table presents the nonlinear short run estimates of the demand for currency, deposits, monetary base MB, and M1 using quarterly data for the period 1957:I and 1997:II. The scale elasticity of money demand is assumed to be unity. t-ratios
are shown in parentheses. indicate the cases in which the h statistics and ARCH1-statistics are significant at the 5 percent 1 percent level of significance. The short-run parameters are estimated from the following nonlinear specification with the
partial adjustment model: ln~mq
t
5 b
0,s
2 b
1,s
S
i
t l
2 1 l
D
1 b
2,s
ln~mq
t21
Table 4. Short-Run Nonlinear Money Demand Estimates Error Correction Model
MoneyScale a
0,s
a
1,s
l
1
a
2,s
l
2
a
3,s
Log- likelihood h statistics ARCH1
Currency GDP
20.6104 23.8665
20.0370 20.9956
20.3325 21.1879
0.0292 0.6182
20.2421 20.5306
20.1777 24.1458
313.7701 22.4021 1.1957
Currency CONS
20.4372 23.6162
20.0243 20.8228
20.4023 21.2034
0.0217 0.4883
20.2495 20.4343
20.1484 24.0562
317.9059 23.6135 2.3204 Deposits
GDP 0.0020
0.0075 20.1671
20.8114 0.1443
0.5784 0.1889
0.7683 0.1800
0.6812 20.0102
21.4819 384.7783 22.7922
2.9198 Deposits
CONS 0.1193
0.2198 20.3113
20.6937 0.3018
1.0110 0.4181
0.6381 0.3778
1.1560 20.0070
21.1113 385.1746 23.9878
5.3098 MBGDP
20.1100 22.3991
20.0220 21.0799
20.3651 21.4320
0.0140 0.8709
20.4513 21.4508
20.0284 22.3449
391.2972 20.9259 0.8309
MBCONS 20.0793
22.4431 20.0130
20.8773 20.4483
21.4525 0.0080
0.6598 20.5201
21.2835 20.0231
22.4616 402.9537 21.7889
0.7834 M1GDP
20.0669 20.9990
20.1156 21.3917
0.1205 0.5329
0.1154 1.2285
0.1676 0.6472
20.0272 22.4510
399.1715 22.3755 0.7103
M1CONS 20.0221
20.2704 20.1010
21.1247 0.1531
0.5407 0.1261
0.9601 0.2923
0.8520 20.0224
22.4632 402.2433 24.1885 1.8221
Note: This table presents the nonlinear short run estimates of the demand for currency, deposits, monetary base MB, and M1 using quarterly data for the period 1957:I and 1997:II. The scale elasticity of money demand is assumed to be unity. t-ratios
are shown parentheses. indicate the cases in which the h statistics and ARCH1-statistics are significant at the 5 percent 1 percent level of significance. The short-run parameters are estimated from the following nonlinear specification with the error
correction model: D lnm
t
5 a
0,s
1 a
1,s
S
i
t l
t
2 1 l
1
D
1 a
2,s
S
i
t21 l
2
2 1 l
2
D
1 a
3,s
lnm
t21
244 T. G. Bali
Box–Cox restriction: a semi-logarithmic Cagan-type money demand function will be the proper specification if the value of l in equation 15 or if the values of l
1
and l
2
in equation 19 are found to be statistically not different from one whereas if l in the partial
adjustment model or l
1
and l
2
in the error correction model are statistically equal to zero then the demand for real balances is logarithmic in i
t
. In other words, having computed the estimate of l or l
1
and l
2
, the next step is to test whether the true l or true l
1
and l
2
is are statistically different from one or different from zero. To serve the purpose, two different econometric tests—the Wald test and the Likelihood Ratio test—are applied to
the nonlinear money demand equations presented in equations 15 and 19. As demon- strated in Tables 6 and 7, for each monetary aggregate and each scale variable, the
semi-log form is rejected but the double-log form is not at the 5 percent level of
Table 5. Long-Run Money Demand Estimates
MoneyScale Specification
Partial Adjustment Model Error Correction Model
b b
1
a a
1
CURRENCYGDP Semi-log
22.8738 263.750
3.6930 5.3220
22.8799 257.203
3.5656 4.5975
CURRENCYGDP Double-log
23.7786 244.488
0.2335 8.1587
23.7598 235.934
0.2278 6.4644
CURRENCYCONS Semi-log
22.4167 244.056
3.8785 4.5741
22.4210 240.516
3.7904 4.1057
CURRENCYCONS Double-log
23.3707 231.810
0.2466 6.9084
23.3605 226.583
0.2438 5.7209
DEPOSITSGDP Semi-log
21.6788 26.1138
72.317 1.8196
22.0200 25.0461
49.268 1.0818
DEPOSITSGDP Double-log
25.1160 22.8566
0.5743 1.7077
24.5552 22.0930
0.4207 1.0577
DEPOSITSCONS Semi-log
21.1866 23.1346
99.852 1.5569
21.5880 22.9395
79.748 1.0522
DEPOSITSCONS Double-log
26.0607 21.9604
0.8161 1.4377
25.9193 21.4208
0.7279 1.0004
MBGDP Semi-log
22.3799 217.014
7.0645 3.0977
22.4255 214.267
6.5814 2.4314
MBGDP Double-log
24.0635 213.353
0.4388 4.3868
23.9913 29.5724
0.4055 2.9649
MBCONS Semi-log
21.8921 210.596
8.6147 2.7901
21.9239 29.5052
8.3780 2.4128
MBCONS Double-log
23.9166 29.2631
0.5277 3.8580
23.9129 27.1972
0.5164 2.9674
M1GDP Semi-log
21.3326 210.383
7.2649 3.5370
21.4471 27.7541
6.2057 2.2876
M1GDP Double-log
23.0405 210.642
0.4454 4.7679
22.9308 27.4081
0.3916 3.0054
M1CONS Semi-log
20.8704 25.2453
8.6020 3.0690
20.9750 24.3603
7.8865 2.2421
M1CONS Double-log
22.8662 27.1013
0.5205 4.0315
22.8325 25.3913
0.4911 2.9552
Note: This table presents the long-run parameter estimates of the demand for currency, deposits, monetary base MB, and M1 with the partial adjustment and error correction models. The long-run parameters are unscrambled from the short-run
estimates: b 5 b
0,s
12b
2,s
and b
1
5 b
1,s
12b
2,s
are obtained from ln mq
t
5 b
0,s
2 b
1,s
i
t
1 b
2,s
ln mq
t21
or ln mq
t
5 b
0,s
2 b
1,s
ln i
t
1 b
2,s
ln mq
t21
a 5 2a
0,s
a
3,s
and a
1
5 2a
2,s
a
3,s
are obtained from D ln m
t
5 a
0,s
1 a
1,s
D i
t
1 a
2,s
i
t21
1 a
3,s
ln m
t21
or Dln m
t
5 a
0,s
1 a
1,s
D ln i
t
1 a
2,s
ln i
t21
1 a
3,s
ln m
t21
Welfare Cost of Inflation 245
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
