IV. Empirical Results
Preliminary Results
Our objective was to estimate equation 5 and to examine how the coefficients evolved over time. We are particularly interested in the relationship between the coefficients and
the trend volume ratios used to proxy liquidity. Due to the unavailability of data on the quantity of commercial paper outstanding prior to January 1966, we used this as the
starting date for our sample. Column 1 of Table 2 presents results for the basic model, estimated with nonlinear least squares and a first-order serial correlation correction to the
errors r is the serial correlation coefficient.
17
Several important findings emerged. First, the coefficient estimates generally conformed to theory and previous empirical
work. The coefficient on SLOPE was positive and highly significant, suggesting that tight monetary policy is associated with a higher paper-bill spread. The weak link between the
BAA-AAA quality spread is also consistent with previous work [see Bernanke 1990; Friedman and Kuttner 1993]. The positive relationship between conditional interest rate
volatility and the spread is a novel finding. It implies that the spread contains a liquidity premium which is sensitive to interest-rate uncertainty. Finally, growth of aggregate
inventories was associated with a rising spread.
17
As discussed below, the error terms exhibited heteroskedasticity as well as serial correlation. To obtain consistent estimates for the covariance matrix of the coefficients and robust standard errors in this case, the
nonlinear least squares procedure in RATS was used along with the ROBUSTERRORS option.
Figure 2. Log of bill-paper volume ratio and polynomial trend. 368
J. P. Ferderer et al.
It is well known that a major structural shift in U.S. money markets took place in 1979 when the Fed began to target nonborrowed reserves. To examine whether the reduced
form parameters changed over the sample, we conducted a Chow test for parameter stability. The x
2
statistic CHOW in column 1 allows us to reject the null hypothesis of parameter stability. Thus, it appears that the coefficients had significantly different values
prior to January 1979 than they did after this date. To see precisely how the coefficients evolved over the full sample, we estimated the
reduced-form model using rolling regressions. The model was initially estimated over 1961:01–77:12, and then observations were added and dropped one at a time as we
moved through the sample. Figure 3 illustrates the 95 confidence bands for each of the coefficients.
Panel A shows that the coefficient on SLOPE experienced the most dramatic and consistent change in value over the sample, falling from values between .20 and .32 to
almost zero by the 1990s. Instead of taking on discretely different values between 1979 and 1983—as would be expected if the monetary policy regime shift lay behind the
parameter instability detected in Table 2—the coefficient fell gradually over the 1980s. This gradual decline is consistent with the hypothesis that increased liquidity of commer-
cial paper made the paper-bill spread less sensitive to changes in monetary policy.
The coefficient on the quality spread also fell during the 1980s, but was not highly significant to begin with, while the impact of inventory growth on the spread did not
change much over the sample. In contrast, panel D shows that interest-rate uncertainty actually had a greater impact on the spread beginning in the mid-1980s. This last result is
clearly inconsistent with the idea that increased liquidity of the paper market made the
Table 1. Stationarity Tests
y
t
5 a 1 ry
t21
1
O
i51 12
Dy
t2i
1 u
t
or y
t
5 a 1 dt 1 ry
t21
1
O
i51 12
Dy
t2i
1 u
t
Series Sample
Z
r
ADF Exclusion Tests
r 5 1 a 5 0
r 5 1 d 5 0
SPREAD 1961–1994
255.9 254.8
7.1 —
SLOPE 1961–1994
230.0 232.3
4.7 —
QUAL 1961–1994
214.8 215.3
2.6 —
INV 1961–1994
28.6 216.1
— 2.9
DINV 2433.9
2119.9 12.3
— UNCERT
1961–1994 227.0
214.0 2.5
— Q
B
Q
P
1966–1994 212.0
275.4 —
7.5
Note: Z
r
is the Phillips-Perron Z statistic computed using 12 lagged covariances; ADF is the augmented Dickey-Fuller r statistic obtained using 12 lags; a, r and d are coefficients on the constant term, lagged dependent variable, and time trend,
respectively; and T is the number of observations from the unit root regression. Significance at 1, 5 and 10 levels given by , and , respectively.
Critical values from Hamilton 1994.
Increasing Liquidity of the Paper-Bill Spread 369
paper-bill spread less sensitive to uncertainty. However, as we discuss below, this result is likely due to the fact that SLOPE reflects information about interest-rate uncertainty.
To formally examine whether the Fed’s policy shift in late 1979 affected the reduced- form coefficients, the model was re-estimated with five additional variables included: a
dummy variable that has values of 1 between October 1979 and October 1982 0 otherwise, and each of the explanatory variables interacted with this dummy variable.
Column 2 of Table 2 shows results for this model. Two findings merit discussion. First, the x
2
statistic, EXCLUDE1, suggests that we cannot reject the hypothesis that the coefficients on the slope dummies are jointly equal to zero. This finding provides evidence
that the coefficients did not take on different values over the period 1979 –1982. Second, the CHOW statistic shows that the coefficients continued to be unstable even after
controlling for the policy regime shift.
Table 2. Reduced-Form Models for the Paper-Bill Spread Sample: 1966:1–1994:12
Nonlinear Least Squares Two-Stage Nonlinear
Least Squares 1
2 3
4 5
Constant .011
.011 .010
.010 .011
5.09 5.26
4.98 4.08
4.62 SLOPE
.165 .201
.039 .026
.036 6.29
4.82 1.25
1.02 1.42
DINV .001
.001 .001
.000 .000
2.22 1.88
1.56 0.18
0.65 QUAL
2.063 2.075
2.053 2.100
2.179 0.55
0.74 0.39
0.85 1.30
UNCERT .001
.001 .001
.001 .001
2.76 2.61
2.40 1.83
1.74 SLOPE z Q
B
Q
P T
. . . . . .
.248 .217
.182 3.51
4.00 3.74
DINV z Q
B
Q
P T
. . . . . .
.000 2.001
2.001 0.10
1.00 0.91
QUAL z Q
B
Q
P T
. . . . . .
.098 .030
.130 0.47
0.16 0.65
UNCERT z Q
B
Q
P T
. . . . . .
2.000 .000
.000 0.01
0.81 0.21
r .70
.78 .74
.69 .69
11.83 11.83
10.71 8.40
7.74 EXCLUDE1
. . . 3.88
4.61 12.87
8.93 EXCLUDE2
. . . . . .
14.28 17.41
20.64 CHOW
4.73 2.65
1.73 0.78
1.07 HETERO
11.00 11.09
14.51 9.97
4.36 DW
2.00 2.03
2.07 2.07
2.07 R
2
.82 .82
.83 .78
.79
Notes: Numbers in parentheses are t statistics constructed with standard errors that are robust to heteroskedasticity. EXCLUDE1 is a x
2
statistic to test the null hypothesis that coefficients on variables created by interacting the four explanatory variables with the 1979:10–1982:10 dummy are jointly equal to zero. EXCLUDE2 is a x
2
statistic used to test the null hypothesis that the coefficients on variables created by interacting the four explanatory variables with the trend value of the bill-paper
quantity ratio are jointly equal to zero. CHOW is an F statistic used to test for structural stability of the model’s coefficients with the break-date set at 1979:01. HETERO is a x
2
statistic to test for heteroskedasticity of the model’s disturbance term linked to the trend bill-paper quantity ratio.
Significance at 1, 5 and 10 levels given by , , and , respectively.
370 J. P. Ferderer et al.
To directly test whether increased liquidity of the paper market was responsible for the parameter instability, the four explanatory variables SLOPE, QUAL, DINV, and UN-
CERT were multiplied by the polynomial trend of the volume ratio and these interaction terms were added to the model presented in column 2. The results, reported in column
3, indicate four important findings. First, the x
2
statistic, EXCLUDE2, allows us to reject the hypothesis that the coefficients on the interaction terms are jointly equal to zero.
Second, the coefficient on SLOPE z Q
B
Q
P T
was positive and highly significant. Third, the relatively low CHOW statistic compared to columns 1 and 2 suggests that the
model’s parameters were more stable once we controlled for the impact that rising liquidity of the paper market had on the model’s coefficients. Finally, the x
2
statistic HETERO, which tests for heteroskedasticity linked to the trend volume ratio, was highly
significant as it is in columns 1 and 2. Taken together, these findings suggest that increased liquidity of commercial paper made the spread less sensitive to its determinants.
One potential problem with this conclusion is that the righthand-side variables in column 3 may have been endogenous as of time t. For example, forces not picked up by
the explanatory variables could have raised the spread and led to a decline in commercial paper issuance. In this case, the interaction terms are contemporaneously correlated with
the error term and the coefficient estimates are biased. To examine whether this presents a problem, the model in column 3 was reestimated with instrumental variables. The
Figure 3. 95 confidence bands for rolling regression coefficients.
Increasing Liquidity of the Paper-Bill Spread 371
instruments were the twelve monthly lags of each explanatory variable. The results, presented in column 4, were similar to those in column 3, with two exceptions. First,
those in column 4 suggest that the coefficients were significantly different for the period 1979:10 –1982:10. Second, once we accounted for coefficient variation due to the mon-
etary policy regime shift and rising liquidity of the paper market, the coefficients from the reduced-form model were stable.
Finally, column 5 of Table 2 allows us to examine the robustness of our findings to a different proxy for commercial paper liquidity. In particular, the model in column 5
used the 12-month moving average of the log ratio of bills to paper volumes outstanding to proxy paper liquidity. Once again, the results suggest that increased paper market liquidity
caused the relationship between the paper-bill spread and its determinants to weaken.
Decomposing
The results in Table 2 generally support the hypothesis that increased liquidity of the paper market has diminished the ability of the spread to reflect information contained in its
determinants. Nevertheless, the small and insignificant t statistics associated with three of the four interaction terms shown in columns 3–5 are inconsistent with this explanation.
That is, if increased paper market liquidity is responsible for the diminished predictive ability of the spread, then UNCERT z Q
B
Q
P T
and the other interaction terms should also have positive and significant coefficients.
One possible explanation for this inconsistency is that SLOPE embodies information contained in the other explanatory variables. That is, the slope of the term structure not
only gauges the stance of current monetary policy, but also reflects beliefs about future monetary policy through expected real interest rates, expectations about future economic
activity through expected inflation premia, and interest-rate uncertainty through risk premia [see Estrella and Hardouvelis 1989; Ferderer 1993]. Consequently, we may
not be able to isolate the direct impact which uncertainty or other factors have on the spread because regression techniques only use variation unique to a regressor when
calculating its coefficient.
To examine whether this multicollinearity problem produced the inconsistencies ob- served above, we regressed SLOPE on interest-rate uncertainty and used the residual from
this regression SLOPER to measure the stance of monetary policy.
18
If the term structure contains a risk premium and becomes steeper when interest-rate uncertainty rises, this
premium should not be reflected in SLOPER. The results obtained when SLOPE was replaced by SLOPER are presented in Table 3.
The results in Table 3 show that interest-rate uncertainty now has a dramatically more significant impact on the spread than it did in Table 2 across the different models. Figure
4 displays the rolling regression results using the model in column 1 of Table 3. In contrast to Figure 3, we see that interest-rate uncertainty had a positive and significant
impact on the spread during the early part of the sample, and that this effect dissipated during the 1980s and early 1990s. This finding provides evidence that increased paper
market liquidity over the 1980s reduced the ability of the spread to reflect interest-rate uncertainty.
18
This approach has been used in the finance literature. For example, to estimate a “stock market factor” unrelated to his other four factors, Kramer 1994 used the residual from a regression of a stock market index
on his first four factors.
372 J. P. Ferderer et al.
The results in columns 3–5 of Table 3 confirm this visual impression. Note that the coefficient on the variable constructed by multiplying interest-rate uncertainty and the
volume ratio—as well as coefficients on interaction variables created with SLOPE and QUAL—were positive and significantly different from zero. As the ratio of bill to paper
volume fell, so do did the coefficients relating the spread to three of its four determinants. Also, the CHOW statistic suggests that the parameters were stable over the sample period
once we controlled for the liquidity effect. Taken together, these findings provide additional evidence that increased liquidity of commercial paper during the 1980s reduced
the sensitivity of the spread to its determinants.
Table 3. Reduced-Form Models for the Paper-Bill Spread Sample: 1966:1–1994:12
Nonlinear Least Squares Two-Stage Nonlinear
Least Squares 1
2 3
4 5
Constant .017
.019 .018
.016 .016
6.57 6.13
6.76 6.17
6.40 SLOPER
.165 .201
.071 .062
.048 6.31
4.92 2.41
2.38 1.90
DINV .001
.001 .000
.000 .000
2.24 1.96
1.21 0.07
0.48 QUAL
2.066 2.066
2.251 2.265
2.310 0.57
0.65 1.72
2.04 2.17
UNCERT .004
.005 .003
.003 .003
6.57 5.47
5.22 4.21
4.22 SLOPE z Q
B
Q
P T
. . . . . .
.214 .160
.179 3.73
3.31 3.70
DINV z Q
B
Q
P T
. . . . . .
.000 2.001
2.001 0.52
0.65 0.62
QUAL z Q
B
Q
P T
. . . . . .
.410 .281
.371 1.71
1.31 1.67
UNCERT z Q
B
Q
P T
. . . . . .
.002 .001
.002 2.57
1.81 2.49
r .78
.78 .74
.70 .69
11.78 11.92
10.96 8.55
7.81 EXCLUDE1
. . . 3.83
5.07 13.03
9.89 EXCLUDE2
. . . . . .
15.31 12.45
19.09 CHOW
4.72 2.64
1.63 1.07
1.04 HETERO
11.35 11.25
14.41 10.67
4.13 DW
2.00 2.05
2.07 2.06
2.07 R
2
.82 .82
.83 .78
.79
Notes: Numbers in parentheses are t statistics constructed with standard errors that are robust to heteroskedasticity. EXCLUDE1 is a x
2
statistic to test the null hypothesis that coefficients on variables created by interacting the four explanatory variables with the 1979:10–1982:10 dummy are jointly equal to zero. EXCLUDE2 is a x
2
statistic used to test the null hypothesis that the coefficients on variables created by interacting four explanatory variables with the trend value of the bill-paper quantity
ratio are jointly equal to zero. CHOW is an F statistic used to test for structural stability of the model’s coefficients with the break-date set at 1979:01. HETERO is a x
2
statistic to test for heteroskedasticity of the model’s disturbance term linked to the trend bill-paper quantity ratio.
Significance at 1, 5 and 10 levels given by , , and , respectively.
Increasing Liquidity of the Paper-Bill Spread 373
V. Conclusion
Kategori