Next, I formulated the VARs where all the variables are I0, and the vector error correction model VECM where all the variables are I1. I then tested for the indepen-
dent cointegrating vectors among the non-stationary variables in the VECM for the whole sample period. The analysis was conducted using trace tests as specified by Johansen
1988 at 4, 6, 8, 10, and 12 lags. Table 2 suggests there are four different stochastic trends at the 5 significance level and, hence, one independent cointegrating vector.
IV. Estimation Procedure
Model Specification
In line with the initial work of Christiano and Eichenbaum 1991, I specified a baseline VAR which includes the variables in levels as follows:
Model A M
t
5 constant 1 A
mm
~L M
t
1 A
ym
~LY
t
1 A
pm
~L P
t
1 A
cm
~LCP
t
1 A
nm
~L N
t
1 e
m
;
Table 2. Johansen’s Test on Five-Variable System 1960:01–1993:12
Number of Lags
Trace Statistics
Null Hypothesis 4
0.6557 There is at least 1
stochastic trend 6
0.9471 8
1.2613 10
0.7567 12
0.9826 4
4.2176 There are at least
2 stochastic trends 6
3.7963 8
4.5914 10
4.4018 12
4.7456 4
15.6128 There are at least
3 stochastic trends 6
14.6898 8
15.7184 10
13.8973 12
11.8791 4
34.9006 There are at least
4 stochastic trends 6
28.2742 8
28.7907 10
27.5587 12
35.4057 4
116.6594 There are at least
5 stochastic trends 6
82.7605 8
79.9170 10
66.8099 12
80.3278 Estimates of the Error Correction Term coin:
Coin
t
5 3.957M
t21
2 3.341Y
t21
1 646.278DP
t21
2 3.464CP
t21
1 .166N
t21
.
Denotes significance at the 5 level.
Liquidity Effect, Stationarity, and Outliers 307
Y
t
5 constant 1 A
my
~L M
t
1 A
yy
~LY
t
1 A
py
~L P
t
1 A
cy
~LCP
t
1 A
ny
~L N
t
1 e
y
; P
t
5 constant 1 A
mp
~LM
t
1 A
yp
~LY
t
1 A
pp
~LP
t
1 A
cp
~LCP
t
1 A
np
~LN
t
1 e
p
; CP
t
5 constant 1 A
mc
~LM
t
1 A
yc
~LY
t
1 A
pc
~LP
t
1 A
cc
~LCP
t
1 A
nc
~LN
t
1 e
c
; N
t
5 constant 1 A
mn
~LM
t
1 A
yn
~LY
t
1 A
pn
~LP
t
1 A
cn
~LCP
t
1 A
nn
~LN
t
1 e
n
, where the number of lags is K 1 1 the equivalent of K lags in difference, and e is the
orthogonal innovation or the exogenous shock in each equation. The economic rationale for placing m first M rule is that innovations in non-borrowed reserves are assumed to
be independent of current Y, P, CP, and N. This identification scheme is consistent with Barro 1981, Mishkin 1982, King 1982, Leeper 1992, Strongin 1992, Christiano
and Eichenbaum 1991, 1992b and Christiano et al. 1994.
6
To correct for the stationarity of the data, I included the stationary presentation of the variables in the VARs where all the variables are I0. I also included the one-error
correction terms calculated from the whole sample period extending from 1960:01 to 1993:12. The importance of including the error correction terms in the VARs was pointed
out by Engle and Granger 1987, p. 259, who stated that:
Thus vector autoregressions estimated with cointegrated data will be mis-specified if the data are differenced, and will have omitted important constraints if the data are used in levels. Of course, these
constraints will be satisfied asymptotically but efficiency gains and improved multistep forecasts may be achieved by imposing them. [Engle and Granger 1987, p. 259]
In all of the VARs, I also included identities to define the growth rate of each variable as the difference between the current and lagged value of its level. The main reason for
including these identities in the VARs was to restrict the long-run movements of the growth rate of each variable to follow the long-run movements in its level. In summary,
the empirical model used to examine the existence and the stability of the liquidity effect can be stated as follows:
Model B DM
t
5 constant 1 A
mm
~LDM
t
1 A
ym
~LDY
t
1 A
pm
~LD
2
P
t
1 A
cm
~LDCP
t
1 A
nm
~LDN
t
1 a
m
coin
t
1 e
m
; DY
t
5 constant 1 A
my
~LDM
t
1 A
yy
~LDY
t
1 A
py
~LD
2
P
t
1 A
cy
~LDCP
t
1 A
ny
~LDN
t
1 a
y
coin
t
1 e
y
; D
2
P
t
5 constant 1 A
mp
~LDM
t
1 A
yp
~LDY
t
1 A
pp
~LD
2
P
t
1 A
cp
~LDCP
t
1 A
np
~LDN
t
1 a
p
coin
t
1 e
p
; DCP
t
5 constant 1 A
mc
LDM
t
1 A
yc
LDY
t
1 A
pc
LD
2
P
t
1 A
cc
LDCP
t
1 A
nc
LDN
t
1 a
c
coin
t
1 e
c
;
6
Strongin 1992 and Christiano and Eichenbaum 1991 found that placing Y and P before M and N in the VARs had no effect on the responses of N to innovations in M.
308 H. S. Guirguis
DN
t
5 constant 1 A
mn
~LDM
t
1 A
yn
~LDY
t
1 A
pn
~LD
2
P
t
1 A
cn
~LDCP
t
1 A
nn
~LDN
t
1 a
n
coin
t
1 e
n
; DM
t
5 M~t 2 M~t 2 1; DY
t
5 Y~t 2 Y~t 2 1; DP
t
5 P~t 2 P~t 2 1; D
2
CP
t
5 DCP~t 2 DCP~t 2 1; DN
t
5 N~t 2 N~t 2 1, where L is the first lag operator; AL 5 a
1
L 1 a
2
L
2
1 . . . 1 a
k
L
K
; D is the first difference operator, and coin refers to the error correction terms calculated from the characteristic
vector corresponding to the canonical correlation in the Johansen 1988 test: Coin
t
5 ~3.957 M
t21
2 ~3.341Y
t21
1 ~646.278DP
t21
2 ~3.464CP
t21
1 ~.166 N
t21
.
Estimation Technique
I started my analysis by estimating the impulse response functions of the funds rate to innovations in the non-borrowed reserve, as specified by the baseline Model A for the
whole sample period, extending from 1960:1 to 1993:12, at one- to twelve-month horizons. I then used the bootstrapping technique to construct 90 confidence intervals
for the responses where the number of draws is 100.
To examine the existence and the stability of the liquidity effect over the sample period extending from 1960:1 to 1993:12, I estimated the rolling impulse response functions of
the funds rate in Model B with a ten-year window.
7
I began by estimating the responses for the period 1960:1 to 1970:1 at one- to twelve-month horizons. Then, I dropped and
added one month at a time to the starting and the ending dates, respectively. I repeated the process to construct the responses until I reached the end of the sample, where the starting
and the ending date are 1983:12 and 1993:12, respectively. The main advantage of the rolling window regressions is that the responses are more sensitive to including or
excluding observations from the data set, which helps in locating the changes in the causality between money and the interest rate. Finally, to test the sensitivity of my results
to the number of lags in the VARs, I ran all the regressions with 4, 6, 8, 10, and 12 lags for each variable.
V. Empirical Results
