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
In a number of recent papers, the importance of various interest-rate measures as indicators of the stance of monetary policy has been emphasized. In this section, the
relevance of distinctions among unanticipated expansionary, unanticipated contractionary, and anticipated policy, when the indicator of monetary policy is taken to be spread, is
investigated.
21
Spread was regressed on four-lagged values of itself and on four-lagged values of a number of economic variables. These variables were GM, GY, GB, UR, FEBS,
18
Cover 1992 noted the non-neutrality of money for the period 1951:I–1987:IV. However, because the coefficients on the GM
t 1
terms were of the wrong sign in the presence of anticipated money terms, Cover’s preferred regression equation is one in which anticipated money growth terms were excluded. Note that the main
finding of Cover concerning an asymmetry between positive and negative money shocks in explaining movement in output continues to be confirmed in this paper.
19
Cover 1992 also reported a similar result when anticipated money was included in the output equation [see Cover 1992, Tables VI and VII, pp. 1273, 1275]. He found that the sums of coefficients on the positive
shocks SUMPOS and on negative shocks SUMNEG were not statistically significant at the 0.05 level. When anticipated money terms did not appear in the output equation, Cover 1992, pp. 1269–70 found that
SUM NEG was statistically significant at the 0.01 level and that SUMPOS was insignificant.
20
Frydman and Rappoport 1987 introduced these dummy variables to test the robustness of tests of AUDI. They pointed out that the intercept dummy was introduced to catch the observation that money growth rose
appreciably during the early 1960s, and the slope coefficients on the first and second lags of GM were allowed to change after 1971.III to capture structural shifts associated with the collapse of the Bretton Woods regime.
21
Spread was measured by the difference between the 3-month commercial paper rate and the 3-month Treasury bill rate from 1971:II. Prior to 1971:II, the 6-month commercial paper rate was used. The spread series
was found to be level stationary.
ExpansionaryContractionary Monetary Policy
119
and GDP inflation GDINF.
22
GY , GB, and GDINF were not statistically significant for
1949:II–1992:II. Thus, four-lagged values of GM, UR, and FEBS appear along with four-lagged values of spread in the forecasting equation for spread.
To begin with, four-lagged values of the dependent variable, GY
t
, and current and four-lagged values of anticipated change, and positive and negative innovations in spread
appear in the output equation.
23
A positive negative surprise in spread indicates that spread was greater less than expected and, hence, that monetary policy was more
contractionary expansionary than expected. The coefficients on the monetary policy variables should be negative at least at first. To avoid confusion, MPI
t e
, MPI
t u1
, and MPI
t u2
refer to anticipated, unexpected expansionary, and unexpected contractionary policy, respectively.
The results of joint estimation of equations for spread and for output for the period 1950:II–1992:II appear in Tables 6 and 7, respectively. Sets I and II are again estimates
of equations 1 and 2, and of equations 1 and 3. In the spread equations in Table 6, it can be seen that increases in the rate of money growth and in the budget surplus tended
22
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. This was the method employed by Mishkin 1982, p. 30.
23
Four lags in the spread terms are indicated by AIC from examination of the output equation before applying a joint estimation. The residuals of the output equation do not show first-order or higher-order serial
correlation.
Table 6.
Monetary Policy Equations with Spread as Monetary Policy Indicator: Nonlinear Joint Estimation 1950:II–1992:II
standard errors in parentheses
Set I Set II
Variable Coefficient
p Value
Coefficient p
Value Constant
0.200 0.077 0.0098
0.147 0.099 0.1386
MPI {1}
0.630 0.055 0.0000
0.690 0.073 0.0000
MPI {2}
20.038 0.067 0.5739
20.083 0.089 0.3512
MPI {3}
0.076 0.067 0.2556
0.066 0.089 0.4544
MPI {4}
0.057 0.053 0.2885
0.168 0.078 0.0313
UR {1}
20.004 0.047 0.9331
20.122 0.061 0.0445
UR {2}
0.118 0.080 0.1422
0.272 0.110 0.0136
UR {3}
20.336 0.085 0.0001
20.356 0.112 0.0015
UR {4}
0.212 0.048 0.0000
0.191 0.061 0.0018
FEBS {1}
0.427 0.109 0.0001
0.320 0.135 0.0176
FEBS {2}
20.036 0.133 0.7896
0.182 0.163 0.2659
FEBS {3}
20.485 0.133 0.0003
20.597 0.180 0.0008
FEBS {4}
0.170 0.127 0.1830
0.167 0.155 0.2823
GM {1}
0.038 0.024 0.1200
0.071 0.028 0.0112
GM {2}
20.015 0.024 0.5376
20.048 0.031 0.1141
GM {3}
20.014 0.025 0.5834
0.002 0.030 0.9214
GM {4}
0.086 0.022 0.0002
0.057 0.027 0.0353
Std. error 0.307
0.301 DW
1.933 1.957
R
2
0.534 0.549
Notes: GM{i} 5 log difference in M1 with lag i; UR{i} 5 civilian unemployment rate lagged i time periods; FEBS{i} 5 federal budget surplus lagged i time periods. 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.
120
J. Chu and R. A. Ratti
Table 7.
Output Equations with Spread as Monetary Policy Indicator MPI: Nonlinear Joint Estimation 1950:II–1992:II
standard errors and x
2
statistics in parentheses 1 indicates expansionary shock and 2 indicates contractionary shock
Set I Set II
Variable Coefficient
p Value
Variable Coefficient
p Value
Constant 0.750 0.298
0.0119 Constant
1.216 0.288 0.0000
GY {1}
0.372 0.083 0.0000
GY {1}
0.210 0.085 0.0137
GY {2}
0.131 0.082 0.1146
GY {2}
0.102 0.083 0.2178
GY {3}
20.193 0.088 0.0282 GY
{3} 20.169 0.085 0.0469
GY {4}
20.054 0.081 0.5054 GY
{4} 20.062 0.082 0.4529
MPI
e
1.401 0.728 0.0543
MPI
e
1.676 0.741 0.0237
MPI
e
{1} 22.739 0.954 0.0041
MPI
e
{1} 21.981 0.877 0.0238
MPI
e
{2} 0.741 0.928
0.4253 MPI
e
{2} 0.081 0.795
0.9185 MPI
e
{3} 0.605 0.846
0.4749 MPI
e
{3} 20.591 0.760 0.4365
MPI
e
{4} 20.296 0.495 0.5502
MPI
e
{4} 0.093 0.489
0.8487 MPI
u1
20.631 0.574 0.2721 MPI
u
20.714 0.218 0.0010 MPI
u1
{1} 24.435 0.818 0.0000
MPI
u
{1} 21.915 0.598 0.0013
MPI
u1
{2} 2.734 0.862
0.0015 MPI
u
{2} 20.043 0.583 0.9410
MPI
u1
{3} 0.014 0.829
0.9866 MPI
u
{3} 0.005 0.529
0.9909 MPI
u1
{4} 0.201 0.758
0.7912 MPI
u
{4} 0.722 0.510
0.1571 MPI
u2
21.057 0.356 0.0030 MPI
u2
{1} 0.044 0.588
0.9398 MPI
u2
{2} 20.898 0.589 0.1276
MPI
u2
{3} 20.330 0.559 0.5551
MPI
u2
{4} 0.086 0.548
0.8761 Hypothesis
Hypothesis MPI
e
{i} 5 0
a
, i 5 0, . . . 4 11.483 0.0425
MPI
e
{i} 5 0
a
, i 5 0, . . . 4 13.684 0.0177
¥ MPI
e
5 0
b
, 0.447
0.5034 ¥ MPI
e
5 0
b
, 5.078
0.0242 MPI
u1
{1} 5 0
a
, i 5 0, . . . 4
37.892 0.0000
MPI
u
{i} 5 0
a
, i 5 0, . . . 4 22.527 0.0004
¥ MPI
u1
5 0
b
, 3.764
0.0523 ¥ MPI
u
5 0
b
, 4.121
0.0423 MPI
u2
{i} 5 0
a
, i 5 0, . . . 4
12.477 0.0287
¥ MPI
u2
5 0
b
, 5.457
0.0194 MPI
u1
{i} 5 MPI
u2
{i}
c
, i 5 0, . . . 4
35.947 0.0000
¥ MPI
u1
5 ¥ MPI
u2 d
0.001 0.9764
MPI
u1
{i} 5 MPI
u2
{i} 5 MPI
e
{i}
c
, i 5 0, 1 . . . 4 46.562 0.0000
MPI
e
{i} 5 MPI
u
{i}
c
, i 5 0, 1 . . . 4
12.782 0.0255
¥ MPI
u1
5 ¥ MPI
u2
5 ¥ MPI
e d
3.647 0.1614
¥ MPI
e
5 ¥ MPI
u d
1.275 0.2588
Std. error 0.712
0.794 DW
2.098 2.092
R
2
0.529 0.412
a
x
2
5-test of the null hypothesis that the coefficients on MPI
e
MPI
u1
, MPI
u2
, or MPI
u
terms are jointly zero.
b
x
2
1-test of the null hypothesis that the sum of the coefficients on the MPI
e
MPI
u1
, MPI
u2
, or MPI
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.
ExpansionaryContractionary Monetary Policy
121
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