to raise spread one quarter later, after which time the effect was eroded, and a rise in the unemployment rate tended to reduce spread after three quarters followed by a reversal in
the fourth quarter. In the output equation in Table 7, the null hypothesis that distinctions among anticipated, unanticipated positive, and unanticipated negative changes in spread is
irrelevant in explaining growth in output SYMMETRY was rejected.
The effects of increasing n for the period ending in 1992:II, and for a period ending in 1979:III, are reported in Table 8. Also, results are presented for a period starting in
1957:III. This sample period was included because it matches the period for which results were available on the federal funds rate as the measure of monetary policy. From Table
8, it can be seen that as lag length increased in the spread variables, the null hypothesis of equality of coefficients on MPI
u1
, MPI
u2
, and MPI
e
continued to be rejected at the 0.01 level.
24
Expansionary monetary policy, signaled by spread, usually had a statistically signifi- cant effect on output in Table 8. The exception was for the sample ending in 1979:III with
n 5 16. It is interesting that contractionary monetary policy signaled by spread was not
usually quite as potent, especially for the sample ending in 1979:III. Consistent with the M1 results, spread as an indicator of monetary policy reinforces the conclusion that
asymmetries among the effects of anticipated, expansionary unanticipated, and contrac- tionary unanticipated monetary policy on aggregate output are of some empirical impor-
tance.
25
V. Federal Funds Rate as Monetary Policy Indicator
The use of change in the federal funds rate as a monetary policy indicator provides an opportunity to test a stimulativecontractionary distinction in the effect on output. Antic-
ipated changes in the federal funds rate are divided into positive anticipated contraction- ary and negative anticipated stimulative components, MPI
e2
and MPI
e1
, respectively. The output equation is given by:
GY
t
5 a
1
O
i5 1
m
a
1i
GY
t2i
1
O
i5 n
b
i u1
MPI
t2i u1
1
O
i5 n
b
i u2
MPI
t2i u2
1
O
i5 n
b
i e1
MPI
t2i e1
1
O
i5 n
b
i e2
MPI
t2i e2
1 W
t
u 1 e
t
. 29
It is now possible to test the following two hypotheses:
26
H SC: No stimulativecontractionary asymmetry given by b
i e1
5 b
i e2
and b
i u1
5 b
i u2
, i 5
1, . . . n. H
AU: No anticipatedunanticipated asymmetry given by b
i e1
5 b
i u1
and b
i e2
5 b
i u2
, i 5
1, . . . n.
24
As a check for robustness, an alternative specification of the spread equation was tried in which four lags of real growth GY and of inflation GDINFL were added to those listed in the spread equation in Table 6.
Results were found to be very similar to those given in Tables 7 and 8 concerning effects of spread as MPI and, thus, are not reported here.
25
In contrast to results when monetary policy was measured by growth in M1, results in Table 8 suggest that anticipated change in spread has, at best, only marginal effects on output except when n 5 4.
26
The authors are grateful to a referee for suggesting this formulation for the AC and AU hypotheses.
122
J. Chu and R. A. Ratti
Table 8.
Test Results of Null Hypotheses When Spread is Monetary Policy Indicator p values reported
Equation Hypothesis
a
Lag Length
b
n 5 4
n 5 8
n 5 12
n 5 16
Spread 1950:II–1979:III SYMMETRY
0.0049 0.0001
0.0001 0.0000
PNDI 0.0026
0.0000 0.0000
0.0000 Un. expansionary
0.0017 0.0179
0.0223 0.4890
Un. contractionary 0.3818
0.3058 0.4120
0.0082 Anticipated
0.0007 0.0704
0.1384 0.4302
With restriction b
i u1
5 b
i u2
, i 5 0, . . . n {Anticipated}
0.0616 0.4415
0.5884 0.9426
Unanticipated 0.2939
0.4106 0.2190
0.4695 AUDI
0.1091 0.5425
0.5453 0.9406
Spread 1950:II–1992:II SYMMETRY
0.0000 0.0000
0.0000 0.0000
PNDI 0.0000
0.0000 0.0000
0.0000 Un. expansionary
0.0000 0.0000
0.0000 0.0000
Un. contractionary 0.0287
0.0503 0.0326
0.0262 Anticipated
0.0425 0.2139
0.0821 0.0801
With restriction b
i u1
5 b
i u2
, i 5 0, . . . n {Anticipated}
0.0177 0.4581
0.4642 0.6535
Unanticipated 0.0004
0.0024 0.0123
0.0527 AUDI
0.0255 0.2089
0.3646 0.5426
Spread 1957:III–1992:II SYMMETRY
0.0000 0.0000
0.0000 0.0000
PNDI 0.0000
0.0000 0.0000
0.0000 Un. expansionary
0.0000 0.0000
0.0000 0.0000
Un. contractionary 0.0053
0.0002 0.0004
0.0000 Anticipated
0.3477 0.3800
0.2576 0.1083
With restriction b
i u1
5 b
i u2
, i 5 0, . . . n {Anticipated}
0.2301 0.2846
0.5347 0.5322
Unanticipated 0.0009
0.0085 0.2314
0.0684 AUDI
0.0547 0.2173
0.5137 0.5372
a
SYMMETRY -distinctions among anticipated, unanticipated positive, and unanticipated negative monetary policy 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 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 is irrelevant. Null hypothesis: b
i u1
5 b
i u2
, i 5 0, 1, . . . n. Un. expansionary refers to unanticipated negative spread null hypothesis is b
i u1
5 0, i 5 0, 1, . . . n. Un. contractionary refers to unanticipated positive spread null hypothesis is b
i u2
5 0, i 5 0, 1, . . . n. Anticipated-null hypothesis is b
i e
5 0, i 5 0, 1, . . . n. 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.
b
For n 5 4, regressions start from 1950:II or 1957:III. As n increases, regressions start at successively later dates.
ExpansionaryContractionary Monetary Policy
123
The change in the federal funds rate is now regressed on four-lagged values of itself and on four-lagged values of a number of economic variables which have been previously
introduced.
27
The variables tried on the righthand side of equation 1 as explanatory variables include four lags of the variables GM, GY, UR, FEBS, and GDINF. Four-lagged
values of each of these variables were retained in the equation explaining spread only if they were jointly significant at the .05 level or stronger. It was found that the lagged
dependent variable, GY, and GDINF were statistically significant.
In the output equation, two-lagged values of the dependent variable, GY, and current and five-lagged values of anticipated and unanticipated positive and negative innovations
in the change in the federal funds rate appear on the basis of AIC. The current and lagged value of the change in the T-bill rate DTBR are also included as explanatory variables
in the output equation.
28
Innovations in the change in the federal funds rate should be negatively associated with real output growth at least, at first.
The federal funds rate equation and the output equation were jointly estimated and the results are presented in Tables 9 and 10. Set I refers to joint estimation of equations 1
and 29, and Set II refers to joint estimation of equations 1 and 3. In the federal funds equations, it can be seen that increases in the rate of real growth raised the change in the
federal funds rate for several quarters, and that an increase in the rate of inflation had the same effect for about two quarters.
27
The level of the federal funds rate is non-stationary and the change in the federal funds rate is stationary.
28
As emphasized by Bernanke and Blinder 1992, when interpreting movement in the federal funds rate, it helps to know the current level of market rates of interest.
Table 9.
Monetary Policy Equations with Change in Federal Funds Rate as Monetary Policy Indicator: Nonlinear Joint Estimation 1957:III–1992:II
standard errors in parentheses
Set I Set II
Variable Coefficient
p Value
Coefficient p
Value Constant
21.122 0.199 0.0000
20.726 0.244 0.0029
MPI {1}
0.069 0.059 0.2402
0.063 0.084 0.4517
MPI {2}
20.300 0.066 0.0000
20.356 0.082 0.0000
MPI {3}
0.034 0.052 0.5138
0.087 0.088 0.3234
MPI {4}
0.027 0.054 0.6103
0.018 0.080 0.8172
GY {1}
0.294 0.059 0.0000
0.373 0.095 0.0000
GY {2}
0.116 0.054 0.0328
0.154 0.089 0.0853
GY {3}
0.216 0.052 0.0000
0.119 0.078 0.1255
GY {4}
0.088 0.050 0.0810
0.002 0.065 0.9716
GDINF {1}
0.250 0.121 0.0395
0.216 0.131 0.0993
GDINF {2}
0.537 0.136 0.0000
0.469 0.167 0.0049
GDINF {3}
20.326 0.124 0.0089
20.039 0.138 0.7738
GDINF {4}
0.009 0.101 0.9193
20.396 0.167 0.0178
Std. error 0.978
0.949 DW
1.930 1.981
R
2
0.238 0.276
Notes: GY{i} 5 log difference in real GDP with lag i; GDINF{i} 5 log difference in GDP-deflator lagged i time periods. In the output equation for Set I, distinctions among the effects of positive and negative anticipated and unanticipated change in
the federal funds rate are recognized. In the output equation for Set II, only a distinction between anticipated and unanticipated change in the federal funds rate is recognized.
124
J. Chu and R. A. Ratti
Table 10.
Output Equations with Change in Federal Funds Rate as Monetary Policy Indicator MPI: Nonlinear Joint Estimation 1957:III–1992:II
standard errors and x
2
statistics in parentheses 1 indicates expansionary policy and 2 indicates contractionary policy
Set I Set II
Variable Coefficient
p Value
Variable Coefficient
p Value
Constant 0.223 0.199
0.0000 Constant
0.285 0.170 0.0941
GY {1}
0.367 0.143 0.0102
GY {1}
0.554 0.225 0.0137
GY {2}
0.325 0.157 0.0390
GY {2}
0.050 0.208 0.8086
DTBR 0.818 0.190
0.0000 DTBR
0.597 0.188 0.0014
DTBR {1}
0.121 0.218 0.5779
DTBR 0.203 0.201
0.3107 MPI
e1
21.152 0.417 0.0058 MPI
e
21.298 0.506 0.0103 MPI
e1
{1} 0.388 0.443
0.3816 MPI
e
{1} 0.618 0.555
0.2656 MPI
e1
{2} 20.429 0.304 0.1582
MPI
e
{2} 20.735 0.458 0.1086
MPI
e1
{3} 20.140 0.282 0.6190
MPI
e
{3} 0.350 0.410
0.3939 MPI
e1
{4} 20.096 0.266 0.7171
MPI
e
{4} 20.147 0.261 0.5708
MPI
e1
{5} 0.010 0.237
0.9663 MPI
e
{5} 20.117 0.155 0.4499
MPI
e2
20.844 0.485 0.0822 MPI
u
20.131 0.156 0.3990 MPI
e2
{1} 21.431 0.611 0.0191
MPI
u
{1} 20.045 0.185 0.8041
MPI
e2
{2} 1.574 0.508
0.0019 MPI
u
{2} 20.671 0.232 0.0039
MPI
e2
{3} 20.340 0.401 0.3956
MPI
u
{3} 0.247 0.279
0.3747 MPI
e2
{4} 0.334 0.396
0.3986 MPI
u
{4} 20.278 0.215 0.1948
MPI
e2
{5} 20.678 0.345 0.0496
MPI
u
{5} 20.200 0.138 0.1477
MPI
u1
20.285 0.207 0.1691 Hypothesis
MPI
u1
{1} 20.128 0.222 0.5633
MPI
e
{i} 5 0
a
, i 5 0, . . . 5 11.459 0.0751
MPI
u1
{2} 20.507 0.205 0.0136
¥ MPI
e
5 0
b
, 7.985
0.0047 MPI
u1
{3} 20.414 0.231 0.0733
MPI
u
{i} 5 0
a
, i 5 0, . . . 5 26.054 0.0002
MPI
u1
{4} 0.128 0.190
0.4987 ¥ MPI
u
5 0
b
, 12.675
0.0003 MPI
u1
{5} 0.011 0.155
0.9401 MPI
u2
20.283 0.186 0.1288 MPI
e
{i} 5 MPI
u
{i}
a
, 7.771
0.2553 MPI
u2
{1} 20.053 0.191 0.7779
¥ MPI
e
5 ¥ MPI
u b
0.347 0.5559
MPI
u2
{2} 20.326 0.175 0.0626
MPI
u2
{3} 20.185 0.201 0.3576
Std. error 0.744
MPI
u2
{4} 0.122 0.176
0.4856 DW
2.028 MPI
u2
{5} 20.535 0.170 0.0016
R
2
0.431 Hypothesis
MPI
e1
{i} 5 0
a
, 14.929
0.0208 ¥ MPI
e1
5 0
b
, 7.969
0.0047 MPI
e2
{i} 5 0
a
, 19.866
0.0029 ¥ MPI
e2
5 0
b
, 5.957
0.0146 MPI
u1
{i} 5 0
a
, 17.419
0.0078 ¥ MPI
u1
5 0
b
, 10.481
0.0012 MPI
u2
{i} 5 0
a
, 23.707
0.0005 ¥ MPI
u2
5 0
b
, 14.168
0.0001 MPI
e1
{i} 5 MPI
e2
{i}
a
19.194 0.0038
¥ MPI
e1
5 ¥ MPI
e2 b
0.001 0.9660
MPI
u1
{i} 5 MPI
u2
{i}
a
i 5 0, 1 . . . 5
7.763 0.2559
¥ MPI
u1
5 ¥ MPI
u2 b
0.038 0.8450
SC : No stimulativecontractionary: MPI
e1
{i} 5 MPI
e2
{i} and MPI
u1
{i} 5 MPI
u2
{i}
c
25.259 0.0136
AU : No anticipatedunanticipated: MPI
e1
{i} 5 MPI
u1
{i} and MPI
e2
{i} 5 MPI
u2
{i}
c
20.913 0.0516
Std. error 0.625
DW 1.994
R
2
0.602
a
x
2
6-test of the null hypothesis for coefficients on variables indicated.
b
x
2
1-test of the null hypothesis for coefficients on variables indicated.
c
x
2
12-test of the null hypothesis for coefficients on variables indicated.
ExpansionaryContractionary Monetary Policy
125
In Table 10, it is reported, based on exclusion tests, that each of the four components of policy had statistically significant effects on output. The cumulative effects were also
each found to be statistically significant. This latter result is different from that obtained when MPI was measured by growth in M1.
Results on the no stimulativecontractionary asymmetry SC and no anticipated unanticipated AU hypotheses are reported at the bottom of Table 10. It was found that
SC was rejected at the 0.0136 level. This result would seem to be based on the finding of
asymmetry in anticipated policy between stimulative and contractionary actions. This follows, as the null hypothesis of b
i e1
5 b
i e2
, i 5 0, 1 . . . 5 was rejected with p value 0.0208, compared to failure to reject the null hypothesis of b
i u1
5 b
i u2
, i 5 0, 1, . . . 5. In addition, it will be noted from Set II, that the exclusion test for anticipated money had a
p value of only 0.0751. Thus, recognition of an asymmetry in anticipated policy would
again seem to be of importance to results. In Table 10, AU was rejected at the 0.0516 level. The results discussed here for n 5 5 generally held for longer lag lengths and are
reported in Table 11.
29
For the purpose of comparison with the results obtained in the earlier part of the paper, results are presented in Table 12 for the federal funds rate, in
which an asymmetry in anticipated policy was not recognized these results can be contrasted with those for spread summarized in Table 8.
In Table 11, asymmetries are to be found in both stimulative versus contractionary policy, and in anticipated versus unanticipated effects. For changes in the federal funds
rate, as a measure of monetary policy, it would seem that an asymmetry in the effects on output of anticipated policy between stimulative and contractionary components is of
some empirical importance.
To illustrate these asymmetries, a simple five-variable VARGY, MPI
u2
, MPI
u1
, MPI
e2
, MPI
e1
was estimated and impulse response functions for GY obtained.
30
The impulse responses of growth in GDP GY to one-standard-error shocks to MPI
u2
and MPI
u1
are shown in Figure 1, and to MPI
e2
and MPI
e1
in Figure 2. In Figure 1, the negative effect of unanticipated contractionary policy was initially somewhat larger in
absolute value than the positive effect of unanticipated stimulative policy. Both effects on GY
fluctuated and decayed fast with eight quarters. In Figure 2, the negative effect of anticipated contractionary policy was larger in absolute value in the first two quarters than
the positive effect of anticipated stimulative policy. MPI
e2
showed a positive effect after two quarters. Thus, it seems that anticipated contractionary policy has a relatively large,
but short-lived, negative effect on GY. The impulse responses from the VAR are consis-
29
Results are not reported for a period ending in 1979:III because there was an inadequate number of degrees of freedom available for test statistics. As a check for robustness for the results over the period 1957:III–1992:II,
an alternative specification of the federal funds rate equation in Table 9 was tried. In addition to four lags of GY and of GDINFL, four lags each of UR, FEBS, and GM were added as explanatory variables in the federal funds
rate equation. The main difference in results concerned unanticipated policy. AU was more likely to be rejected, with p values that the anticipatedunanticipated distinction not being relevant H
AU: b
i e1
5 b
i u1
and b
i e2
5 b
i u2
, i 5 1, . . . n. now being 0.0905 n 5 5, 0.0008 n 5 8, 0.0000 n 5 12, and 0.0000 n 5 16. In addition, the hypothesis of no asymmetry in unanticipated policy H
: b
i u1
5 b
i u2
was also more likely to be rejected with p
values 0.8628 n 5 5, 0.0061 n 5 8, 0.0000 n 5 12, and 0.0000 n 5 16. Results for asymmetry in anticipated policy were similar to those already reported. Given limitations of space, these results are not
reported here.
30
MPI
u2
, MPI
u1
, MPI
e2
, MPI
e1
were obtained for change in the federal funds rate implied by Set I in Tables 9 and 10. The VAR had five lags, constant and deterministic variables, DTBR{0} and DTBR{1}, and was
estimated over the period 1957:III–1992:II. We are grateful to a referee for suggesting impulse response functions be used to illustrate the impact of the components of monetary policy.
126
J. Chu and R. A. Ratti
Table 11.
Test Results of Null Hypotheses with Federal Funds Rate as Measure of Monetary Policy for 1957:III–1992:II
p values reported; x
2
-statistics in parentheses
Hypothesis Lag Length
n 5 5
n 5 8
n 5 12
n 5 16
No Anticipated Expansionary Effect H
o
: b
i e1
5 0, i 5 0, 1 . . . n
a
0.0208 14.929 0.0074 22.483
0.0683 21.236 0.0038 36.534
H
o
: ¥ b
i e1
over i 5 0, 1 . . . n
b
0.0047 7.969 0.0001 14.414
0.0019 9.576 0.0442 4.047
No Anticipated Contractionary Effect H
o
: b
i e2
5 0, i 5 0, 1 . . . n
a
0.0029 19.866 0.0011 27.523
0.0019 32.570 0.0191 31.151
H
o
: ¥ b
i e2
over i 5 0, 1 . . . n
b
0.0146 5.957 0.0014 10.093
0.0064 7.428 0.2394 1.383
No Unanticipated Expansionary Effect H
o
: b
i u1
5 0, i 5 0, 1 . . . n
a
0.0078 17.419 0.0157 20.374
0.0083 28.259 0.0013 39.821
H
o
: ¥ b
i u1
over i 5 0, 1 . . . n
b
0.0012 10.481 0.0001 14.310
0.0002 13.265 0.0146 5.961
No Unanticipated Contractionary Effect H
o
: b
i u2
5 0, i 5 0, 1 . . . n
a
0.0005 23.707 0.0001 33.439
0.0019 32.585 0.0017 39.039
H
o
: ¥ b
i u2
over i 5 0, 1 . . . n
b
0.0001 14.168 0.0001 14.765
0.0037 8.425 0.1335 2.250
No Asymmetry in Anticipated Policy H
o
: b
i e1
5 b
i e2
5 0, i 5 0, 1 . . . n
a
0.0038 19.194 0.0178 20.002
0.0329 23.811 0.0064 34.863
H
o
: ¥ b
i e1
5 ¥ b
i e2
over i 5 0, 1 . . . n
b
0.9660 0.001 0.7835 0.075
0.8094 0.068 0.9297 0.007
No Asymmetry in Unanticipated Policy H
o
: b
i u1
5 b
i u2
5 0, i 5 0, 1 . . . n
a
0.2559 7.763 0.2693 11.094
0.1216 19.047 0.0033 37.012
H
o
: ¥ b
i u1
5 ¥ b
i u2
over i 5 0, 1 . . . n
b
0.8450 0.038 0.9310 0.007
0.8966 0.152 0.4404 0.595
No StimulativeContractionary Asymmetry H
o
SC: b
i e1
5 b
i e2
and b
i u1
5 b
i u2
i 5 0, 1 . . . n
c
0.0136 25.259 0.0538 28.573
0.0062 47.459 0.0003 69.193
No AnticipatedUnanticipated Asymmetry H
o
AU: b
i e1
5 b
i u1
and b
i e2
5 b
i u2
i 5 0, 1 . . . n
c
0.0516 20.913 0.0726 27.350
0.0964 35.743 0.0470 48.906
a
x
2
test with n 1 1 degrees of freedom.
b
x
2
test with one degree of freedom.
c
x
2
test with 2n 1 2 degrees of freedom.
ExpansionaryContractionary Monetary Policy
127
tent with the results noted in Table 11, concerning an asymmetry in anticipated policy between stimulative and contractionary effects.
VI. Conclusion