rejected by failure to account for a possible asymmetry between positive and negative monetary policy surprises. It is also contended that if such an asymmetry exists in effects
on output, taking account of this distinction will affect findings on neutrality. The underlying reason for these results can be seen intuitively by supposing that the
true output equation is given by equation 2. In this case, the error term in equation 3 is defined as:
h
t
5
O
i5 n
~b
i u1
2 k
i u
MPI
t2i u1
1
O
i5 n
~b
i u2
2 k
i u
MPI
t2i u2
1 e
t
. 4
Equation 4 demonstrates that in equation 3, h
t
is not orthogonal to the MPI
t2i u
5MPI
t2i u1
1 MPI
t2i u2
terms when b
i u1
Þ b
i u2
, i 5 0, 1 . . . n. This leads to inconsistent estimators of the parameters in equation 3 and inconsistent test statistics on hypotheses
concerning these parameters.
12
The estimation procedure is as follows. Equations 1 and 2 are estimated by OLS. In equation 2, MPI
t2i u1
and MPI
t2i u2
i 5 0, 1, . . . n have been given by the residuals from equation 1. In this second stage, n is determined by the Akaike 1973 Information
Criterion AIC. The OLS residuals of both equations are used to construct the variance- covariance matrix for the system, and equations 1 and 2 are re-estimated jointly by
nonlinear generalized least-squares, treating the estimated variance-covariance matrix as given. It is assumed that the residuals in the monetary policy equation and in the output
equation are uncorrelated. A new variance-covariance matrix is re-estimated with each new set of coefficient estimates until the change in this estimated matrix is infinitesimal.
13
III. Empirical Results for M1
To separate monetary policy into anticipated and unanticipated positive and negative components, growth in M1 GM is regressed on lagged values of itself, lagged values of
growth in the monetary base GB, lagged values of the unemployment rate UR, lagged growth rates of GDP GY, lagged changes in the T-bill rate DTBR, and lags of the
federal government surplus FEBS.
14
This specification is similar to that in Mishkin 1982, Frydman and Rappoport 1987, and Cover 1992. The growth rate in output is
regressed on lag distributions of MG
e
, MG
u1
, and MG
u2
, and lags of changes in the Treasury-bill rate and growth in output.
15
Results of joint estimation of money and output
12
It should also be noted that inconsistent estimators might be obtained if an asymmetry exists in anticipated policy. However, for measures of monetary policy given by growth in M1 and spread, it is not possible with the
method outlined above to identify stimulative and contractionary components of anticipated policy. This issue is considered when change in the federal funds rate is used as measure of monetary policy.
13
This procedure iterated until the relative change in the value of the function was less than 0.000001. The BHHH algorithm was used for optimization. The resulting estimates are approximately maximum-likelihood
estimates [Mishkin 1982, p. 26]. The coefficient estimates obtained from joint estimation are more efficient because of cross-equation restrictions.
14
Data are from CITIBASE, except for M1 prior to 1959:I. As in Cover 1992, M1 during the third month of the quarter was used as the money supply. Prior to 1959:I, data on M1 obtained from Friedman and Schwartz
1970 was multiplied by 0.990302 the ratio of the M1 series in CITIBASE to the M1 series in Friedman and Schwartz for the period 1959:I–1960:IV.
15
The Treasury-bill rate did not appear in the output equations of Barro and Rush 1980, Mishkin 1982, or Frydman and Rappoport 1987. Results when changes in the Treasury-bill rate were excluded from the output
equation were found to be very similar and, for that reason, are not reported. Cover 1992 reported results on output specifications that both included and excluded lags of changes in the Treasury-bill rate, with similar
ExpansionaryContractionary Monetary Policy
113
equations for n 5 4 appear in Tables 1 and 2 for the period 1951:I–1979:III, and in Tables 1 and 3 for the period 1951:I–1992:II.
16
Money equations are reported in Table 1 and output equations in Tables 2 and 3. In these tables, Set I corresponds to equations 1 and
2, and Set II corresponds to equations 1 and 3.
results on an asymmetry between positive and negative policy shocks. Note that lagged changes in the Treasury-bill rate were found to be statistically significant in the output equations.
16
Results for the period ending in 1979:III are reported, as during October 1979, Fed operating procedures changed and results could be more easily compared with those obtained by Barro and Rush 1980, Mishkin
1982, and Frydman and Rappoport 1987. Results are also reported for the period ending in 1992:II. This provides an update and also facilitates comparison with the work of Cover 1992, whose sample period ended
in 1987:IV. n 5 4 was chosen by AIC applied to the initial OLS estimate of the output equation. Results for higher values of n will be reported.
Table 1.
M1 Growth Equations: Nonlinear Joint Estimation standard errors in parentheses
Variable Set I
Set II Coefficient se.
p Value
Coefficient se. p
Value 1951:I–1979:III
Constant 20.153 0.245
0.5349 0.233 0.180
0.1933 GM
{1} 0.174 0.080
0.0306 0.241 0.085
0.0044 GM
{2} 0.261 0.078
0.0008 0.260 0.089
0.0035 GM
{3} 0.155 0.070
0.0276 0.093 0.077
0.2272 GM
{4} 0.019 0.058
0.7408 20.018 0.066
0.7793 GB
{1} 0.156 0.087
0.0731 0.143 0.086
0.0957 GB
{2} 0.084 0.087
0.3358 0.163 0.095
0.0866 DTBR
{1} 20.349 0.081
0.0000 20.384 0.091
0.0000 UR
{1} 0.064 0.041
0.1189 20.016 0.028
0.5590 FEBS
{1} 0.002 0.004
0.6818 0.001 0.002
0.5836 GY
{1} 20.004 0.034
0.8994 20.006 0.039
0.8670 Std. error
0.544 0.549
DW 1.987
2.057 R
2
0.485 0.475
1951:I–1992:II Constant
0.246 0.174 0.1548
0.332 0.173 0.0551
GM {1}
0.276 0.066 0.0000
0.250 0.070 0.0003
GM {2}
0.222 0.069 0.0013
0.277 0.075 0.0002
GM {3}
20.089 0.069 0.1938
20.098 0.071 0.1681
GM {4}
20.079 0.057 0.1623
20.080 0.058 0.1682
GB {1}
0.129 0.071 0.0664
0.094 0.061 0.1232
GB {2}
0.114 0.073 0.1149
0.093 0.062 0.1295
DTBR {1}
20.399 0.048 0.0000
20.371 0.050 0.0000
UR {1}
0.030 0.029 0.3120
0.015 0.029 0.5819
FEBS {1}
20.002 0.001 0.0816
20.002 0.001 0.0079
GY {1}
0.025 0.043 0.5495
0.031 0.044 0.4685
Std. error 0.713
0.713 DW
2.006 1.923
R
2
0.509 0.509
Notes: GM{i} 5 log difference in M1 with lag i; GB{i} 5 log difference in monetary base with lag i; DTBR{1} 5 change in the T-bill rate lagged one period; UR{1} 5 civilian unemployment rate lagged one time period; FEBS{1} 5 federal budget
surplus lagged one period; GY{1} 5 log difference in real GDP lagged one period. In output equation for Set I, a distinction between the effects of positive and negative money shocks was recognized. This distinction was suppressed in Set II.
114
J. Chu and R. A. Ratti
From the Set I results in Tables 1, 2, and 3, it can be seen that the null hypothesis—that distinctions among the effects of MG
e
, MG
u1
, and MG
u2
on growth in output are irrelevant SYMMETRY—is rejected at the 0.05 level for both time periods. From the Set
II results, it is also apparent that AUDI is also rejected. These results are summarized in the first column of the upper part of Table 4 which brings together a number of results as
Table 2.
Output Equations with Growth in M1 as Monetary Policy Indicator: Nonlinear Joint Estimation 1951:I–1979:III
standard errors and x
2
statistics in parentheses
Set I Set II
Variable Coefficient
p Value
Variable Coefficient
p Value
Constant 0.442 0.255
0.0836 Constant 0.859 0.404
0.0334 GY
{1} 0.327 0.086
0.0001 GY{1} 0.256 0.134
0.0549 DTBR
0.377 0.151 0.0124 DTBR{1}
0.280 0.159 0.0777
DTBR {1}
20.071 0.349 0.8395 DTBR{1} 20.883 0.607 0.1455
GM
e
20.157 0.865 0.8563 GM
e
22.195 1.395 0.1157 GM
3
{1} 1.067 0.567
0.0602 GM
e
{1} 1.486 0.656
0.0234 GM
e
{2} 20.856 0.592 0.1481 GM
e
{2} 0.094 0.724
0.8965 GM
e
{3} 1.451 0.634
0.0221 GM
e
{3} 1.513 0.591
0.0104 GM
e
{4} 21.454 0.461 0.0016 GM
e
{4} 21.080 0.419 0.0099
GM
u2
0.088 0.330 0.7888 GM
u
0.347 0.153 0.0235
GM
u2
{1} 0.490 0.381
0.1987 GM
u
{1} 0.939 0.477
0.0488 GM
u2
{2} 0.043 0.402
0.9142 GM
u
{2} 0.943 0.555
0.0894 GM
u2
{3} 0.202 0.334
0.5449 GM
u
{3} 0.141 0.335
0.6723 GM
u2
{4} 20.771 0.361 0.0329 GM
u
{4} 20.180 0.264 0.4944
GM
u1
0.375 0.284 0.1863
GM
u1
{1} 0.103 0.325
0.7502 GM
u1
{2} 0.137 0.380
0.7192 GM
u1
{3} 20.818 0.328 0.0127
GM
u1
{4} 0.290 0.334
0.3845 Hypothesis
GM
e
{i} 5 0
a
, i 5 0, . . . 4 13.273
0.0209 GM
e
{i} 5 0
a
, i 5 0, . . . 49.860 0.0792
¥ GM
e
5 0
b
, 0.083
0.7729 ¥ GM
e
5 0
b
, 0.330
0.5658 GM
u2
{i} 5 0
a
, i 5 0, . . . 4 5.702
0.3363 GM
u
{i} 5 0
a
, i 5 0, . . . 410.814 0.0552
¥ GM
u2
5 0
b
, 0.005
0.9433 ¥ GM
u
5 0
b
, 3.143
0.0762 GM
u1
{i} 5 0
a
, i 5 0, . . . 4 8.700
0.1217 ¥ GM
u1
5 0
b
, 0.015
0.9014 GM
u2
{i} 5 GM
u1
{i}
c
, i 5 0, . . . 4 8.202 0.1454
¥ GM
u2
5 ¥ GM
u1 d
0.001 0.9695
GM
u2
{i} 5 GM
u1
{i} 5 GM
e
{i}
c
, i 5 0, 1 . . .4 19.744
0.0317 GM
e
{i} 5 GM
u
{i}
c
, i 5 0, 1 . . . 4
12.833 0.0249
¥ GM
u2
5 ¥ GM
u1
5 ¥ GM
e d
0.002 0.9988 ¥ GM
e
5 ¥ GM
u d
2.965 0.0851
Std. error 0.764
0.773 DW
2.126 2.094
R
2
0.432 0.420
a
x
2
5-test of the null hypothesis that the coefficients on GM
e
GM
u1
, GM
u2
, or GM
u
terms are jointly zero.
b
x
2
1-test of the null hypothesis that the sum of the coefficients on the GM
e
GM
u1
, GM
u2
, or GM
u
terms is zero.
c
x
2
5-test and x
2
10-test of joint pairwise equality and of joint triple-wise equality, respectively, of coefficients on variables indicated.
d
x
2
1-test and x
2
2-test of pairwise equality and of triple-wise equality, respectively, of sums of coefficients on variables indicated.
GM
e
{i}, GM
u2
{i}, and GM
u1
{i} represent anticipated, unanticipated negative, and unanticipated positive growth in M1, respectively.
ExpansionaryContractionary Monetary Policy
115
lag distributions of the nominal variables are increased. For example, for n 5 8 and greater, the result noted by Frydman and Rappoport 1987, of the anticipated-
Table 3.
Output Equations with Growth in M1 as Monetary Policy Indicator: Nonlinear Joint Estimation 1951:I–1992:II
standard errors and x
2
statistics in parentheses
Set I Set II
Variable Coefficient
p Value
Variable Coefficient
p Value
Constant 0.746 0.268
0.0054 Constant 0.661 0.264
0.0122 GY
{1} 0.311 0.103
0.0025 GY{1} 0.343 0.121
0.0045 DTBR
0.300 0.064 0.0000 DTBR
0.270 0.065 0.0000
DTBR {1}
20.550 0.294 0.0614 DTBR{1} 20.749 0.292 0.0103
GM
e
21.583 0.689 0.0214 GM
e
22.126 0.740 0.0040 GM
e
{1} 0.840 0.363
0.0207 GM
e
{1} 1.077 0.406
0.0079 GM
e
{2} 0.998 0.351
0.0044 GM
e
{2} 1.277 0.423
0.0025 GM
e
{3} 20.084 0.201 0.6743 GM
e
{3} 20.204 0.234 0.3834
GM
e
{4} 20.157 0.175 0.3695 GM
e
{4} 20.151 0.206 0.4607
GM
u2
0.690 0.193 0.0003 GM
u
0.219 0.090 0.0156
GM
u2
{1} 0.537 0.306
0.0789 GM
u
{1} 0.558 0.283
0.0485 GM
u2
{2} 0.366 0.278
0.1869 GM
u
{2} 0.695 0.289
0.0161 GM
u2
{3} 20.502 0.282 0.0746 GM
u
{3} 20.693 0.251 0.0058
GM
u2
{4} 20.362 0.255 0.1555 GM
u
{4} 20.460 0.227 0.0423
GM
u1
20.189 0.165 0.2493 GM
u1
{1} 0.462 0.297
0.1198 GM
u1
{2} 0.594 0.284
0.0363 GM
u1
{3} 20.676 0.234 0.0038
GM
u1
{4} 20.379 0.231 0.1013
Hypothesis GM
e
{i} 5 0
a
, i 5 0, . . . 4 12.428
0.0293 GM
e
{i} 5 0
a
, i 5 0, . . . 411.518 0.0420
¥ GM
e
5 0
b
, 0.005
0.9434 ¥ GM
e
5 0
b
, 0.525
0.4684 GM
u2
{i} 5 0
a
, i 5 0, . . . 4 19.949
0.0012 GM
u
{i} 5 0
a
, i 5 0, . . . 418.401 0.0024
¥ GM
u2
5 0
b
, 2.946
0.0860 ¥ GM
u
5 0
b
, 1.087
0.2971 GM
u1
{i} 5 0
a
, i 5 0, . . . 4 12.792
0.0254 ¥ GM
u1
5 0
b
, 0.201
0.6538 GM
u2
{i} 5 GM
u1
{i}
c
, i 5 0, . . . 4 9.501 0.0906
¥ GM
u2
5 ¥ GM
u1 d
2.455 0.1171
GM
u2
{i} 5 GM
u1
{i} 5 GM
e
{i}
c
, i 5 0, 1 . . . 4
22.016 0.0150
GM
e
{i} 5 GM
u
{i}
c
, i 5 0, 1 . . . 4
12.487 0.0286
¥ GM
u2
5 ¥ GM
u1
5 ¥ GM
e d
3.140 0.2080 ¥ GM
e
5 ¥ GM
u d
1.067 0.3014
Std. error 0.767
0.786 DW
2.107 2.125
R
2
0.405 0.375
a
x
2
5-test of the null hypothesis that the coefficients on GM
e
GM
u1
, GM
u2
, or GM
u
terms are jointly zero.
b
x
2
1-test of the null hypothesis that the sum of the coefficients on the GM
e
GM
u1
, GM
u2
, or GM
u
terms is zero.
c
x
2
5-test and x
2
10-test of joint pairwise equality and of joint triple-wise equality, respectively, of coefficients on variables indicated.
d
x
2
1-test and x
2
2-test of pairwise equality and of triple-wise equality, respectively, of sums of coefficients on variables indicated.
GM
e
{i}, GM
u2
{i}, and GM
u1
{i} represent anticipated, unanticipated negative, and unanticipated positive growth in M1, respectively.
116
J. Chu and R. A. Ratti
unanticipated distinction being irrelevant for the period 1954:I–1976:IV, comes into play on the first line of Table 4.
17
Note however that these results on the rejection of AUDI contrast sharply with those obtained at longer lags when distinctions among positive shocks, negative shocks, and
anticipated money growth are simultaneously allowed. The null hypothesis that distinc- tions among the three types of monetary change are irrelevant is rejected at the 0.01 level
for n 8 for the period ending in 1979:III. In comparison to the conclusion of Frydman and Rappoport, it appears that distinctions between anticipated and unanticipated changes
in nominal values do matter for explaining movement in output, at least when a distinction is allowed between the impact of positive and negative shocks. This outcome is relatively
stable for both sample periods and over various lag lengths.
As reported in Table 5, at longer lags for both sample periods, the null hypotheses that neither positive money nor negative money surprises have an effect on output is rejected
at the 0.05 level. Thus positive money surprises matter as do negative money surprises. This result seems to differ from that reported by Cover 1992, to the effect that positive
17
Frydman and Rappoport 1987 reported results for a period ending in 1976:IV and for n 7. They stated that results with regard to AUDI would be similar for a period ending in 1979, as was indeed the case for results
reported in Table 4.
Table 4.
Test Results of Null Hypotheses of Irrelevance of Distinctions Among Anticipated, Unanticipated Positive, and Unanticipated Negative Growth in M1 for Explaining Movement in
Real Output p values reported
Equation Hypothesis
a
Lag Length
b
n 5 4
n 5 8
n 5 12
n 5 16
M1 1951:I–1979:III AUDI
0.0249 0.2378
0.2781 0.4979
PNDI 0.1454
0.0119 0.0037
0.0090 SYMMETRY
0.0317 0.0050
0.0018 0.0001
M1 1951:I–1992:II AUDI
0.0286 0.0233
0.0364 0.1146
PNDI 0.0906
0.1671 0.1002
0.0369 SYMMETRY
0.0150 0.0135
0.0215 0.0195
Structural Shifts in Money Equation
c
M1 1951:I–1979:III AUDI
0.0248 0.1870
0.1619 0.1859
PNDI 0.1172
0.0001 0.0000
0.0000 SYMMETRY
0.0232 0.0001
0.0000 0.0000
M1 1951:I–1992:II AUDI
0.1139 0.3654
0.0297 0.0615
PNDI 0.1404
0.0032 0.0040
0.0036 SYMMETRY
0.0701 0.0057
0.0001 0.0005
a
SYMMETRY -distinctions among anticipated, unanticipated positive, and unanticipated negative monetary policy change
are irrelevant. Null hypothesis: b
i e
5 b
i u1
5 b
i u2
, i 5 0, 1, . . . n. AUDI
-distinction between anticipated and unanticipated monetary policy change is irrelevant. Null hypothesis: b
i e
5 b
i u
, i 5 0, 1, . . . n restriction b
i u1
5 b
i u2
, i 5 0, . . . n. PNDI
-distinction between unanticipated positive and unanticipated negative monetary policy change is irrelevant. Null hypothesis: b
i u1
5 b
i u2
, i 5 0, 1, . . . n.
b
For n 5 4, regressions start from 1951:I. As n increases, regressions start at successively later dates.
c
Intercept differs before and after 1963:III, and coefficients on first and second lags of money growth terms differ before and after 1971:III. No Treasury-bill rate variables appear in output equation.
ExpansionaryContractionary Monetary Policy
117
money shocks did not affect output growth, and negative shocks had a highly significant effect in reducing output at least for the period 1951:I–1987:IV. The results of Cover
1992, however, hold in an equation which is not reported here, in which the anticipated money terms were suppressed. Results for the period ending in 1987:IV, when GM
u1
, GM
u2
, and GM
e
terms appear in the output equation, are similar to those for a period ending in 1992:II, and over both periods, money was found to be non-neutral. The
Table 5.
Test of Null Hypotheses of Irrelevance of Unexpected Expansionary, Unexpected Contractionary, and Anticipated M1 Growth for Explaining Movement in Real GDP
Equation Hypothesis
a
Lag Length n 5
4 n 5
8 n 5
12 n 5
16 M1 1951:I–1979:III
Un. expansionary 0.1217
0.0190 0.0006
0.0004 Un. contractionary
0.3363 0.0187
0.0111 0.0013
Anticipated 0.0209
0.0079 0.0137
0.0017 With restriction
b
i u1
5 b
i u2
, i 5 0, . . . n
{Anticipated}
b
0.0792 0.1211
0.0650 0.1147
Unanticipated 0.0551
0.0136 0.0015
0.0020 M1 1951:I–1992:II
Un. expansionary 0.0254
0.0119 0.0110
0.0075 Un. contractionary
0.0012 0.0141
0.0794 0.1555
Anticipated 0.0293
0.0405 0.1328
0.0506 With restriction
b
i u1
5 b
i u2
, i 5 0, . . . n
{Anticipated}
b
0.0420 0.1003
0.2078 0.1463
Unanticipated 0.0024
0.0101 0.0267
0.0722 Structural Shifts in Money Equation
M1 1951:I–1979:III Un. expansionary
0.6226 0.0254
0.0019 0.0102
Un. contractionary 0.0001
0.0001 0.0001
0.0000 Anticipated
0.9771 0.0006
0.0012 0.0000
With restriction b
i u1
5 b
i u2
, i 5 0, . . . n
{Anticipated}
b
0.8746 0.1367
0.0356 0.0172
Unanticipated 0.0002
0.0347 0.0001
0.0003 M1 1951:I–1992:II
Un. expansionary 0.6757
0.0325 0.0228
0.0093 Un. contractionary
0.0158 0.0143
0.0018 0.0047
Anticipated 0.2334
0.4116 0.0355
0.0057 With restriction
b
i u1
5 b
i u2
, i 5 0, . . . n
{Anticipated}
b
0.4259 0.5456
0.1351 0.0736
Unanticipated 0.0387
0.2138 0.0637
0.2654
a
For Un. Expansionary unanticipated positive growth in M1, null hypothesis is b
i u1
5 0, i 5 0, 1, . . . n. For Un. Contractionary unanticipated negative growth in M1, null hypothesis is b
i u2
5 0, i 5 0, 1, . . . n. For Anticipated, null hypothesis is b
i e
5 0, i 5 0, 1, . . . n.
b
Null hypothesis for {Anticipated}: b
i e
5 0, i 5 0, 1, . . . n, given restriction b
i u1
5 b
i u2
, i 5 0, . . . n. Null hypothesis for Unanticipated: b
i u
5 0, i 5 0, 1, . . . n, given restriction b
i u1
5 b
i u2
, i 5 0, . . . n.
118
J. Chu and R. A. Ratti
inclusion of anticipated money in the output equation yielded positive money shocks EXPANSIONARY policy in Table 5 which were statistically significant. Anticipated
money was found, for the most part, to matter, and as noted in Table 5, did so more strongly when a distinction between positive and negative money surprises was recog-
nized.
18
In Tables 2 and 3, for n 5 4, it is reported that the null hypothesis that the sums of the coefficients on positive money shocks, on negative money shocks, and on anticipated
money growth are significantly different from zero could not be rejected at the 0.05 level.
19
This result not reported was robust for various lag lengths and for both sample periods. The implication of alternative specifications for the money equation will now be
briefly considered.
Alternative Specifications of the Equations
Intercept and slope dummy variables will now be introduced into the money equation to account for structural change. This will have the effect of altering the measure of
expectations. Following Frydman and Rappoport 1987, in equation 1, the intercept is allowed to differ before and after 1963:III and the coefficients of each of the variables
GM
t2 1
and GM
t2 2
are allowed to differ before and after 1971:III.
20
It was found that money equations estimated with these changes were much improved. Results under the
heading of “structural shifts in money equation” appear in Tables 4 and 5. There, it can again be seen that for both sample periods, SYMMETRY was rejected over all n, whereas
AUDI could not be rejected except for n 5 4. Other results were similar to those already noted.
IV. Spread as Monetary Policy Indicator