Table 4: Ordinary Least Squares Results (with
Δ
VIX) (time period: 01/03/1990 to 12/31/2018)
Eq.
Δ
TB3M
Δ
VIX
Δ
CRB
Δ
GOLD
Δ
COPPER
Δ
OIL1
Δ
OIL2
Δ
DOLLAR
Const R
2
Δ
UST2Y
4 0.466*** -0.005***
-
-
-
-
-
-
-0.000 0.198
5 0.458*** -0.004*** 0.002***
-
-
-
-
-0.804*** -0.000 0.210
6 0.460*** -0.005***
-
-0.000
-
-
-
-0.722*** -0.000 0.208
7 0.459*** -0.005***
-
-
0.000***
-
-
-0.776*** -0.000 0.209
8 0.458*** -0.005***
-
-
-
0.002***
-
-0.776*** -0.000 0.209
9 0.458*** -0.005***
-
-
-
-
0.002*** -0.786*** -0.000 0.210
Δ
UST3Y
4 0.446*** -0.005***
-
-
-
-
-
-
-0.000 0.167
5 0.437*** -0.005*** 0.003***
-
-
-
-
-0.837*** -0.000 0.180
6 0.441*** -0.005***
-
-0.000
-
-
-
-0.711*** -0.000 0.177
7 0.439*** -0.005***
-
-
0.000***
-
-
-0.790*** -0.000 0.178
8 0.437*** -0.005***
-
-
-
0.003***
-
-0.815*** -0.000 0.180
9 0.438*** -0.005***
-
-
-
-
0.003*** -0.824*** -0.000 0.181
Δ
UST5Y
4 0.402*** -0.006***
-
-
-
-
-
-
-0.000 0.133
5 0.393*** -0.005*** 0.003***
-
-
-
-
-0.748*** -0.000 0.144
6 0.397*** -0.006***
-
-0.000
-
-
-
-0.574*** -0.000 0.139
7 0.395*** -0.006***
-
-
0.000***
-
-
-0.700*** -0.000 0.141
8 0.391*** -0.006***
-
-
-
0.005***
-
-0.750*** -0.000 0.147
9 0.393*** -0.006***
-
-
-
-
0.005*** -0.750*** -0.000 0.146
Δ
UST7Y
4 0.346*** -0.006***
-
-
-
-
-
-
-0.000 0.104
5 0.338*** -0.006*** 0.003***
-
-
-
-
-0.615*** -0.001 0.114
6 0.342*** -0.006***
-
-0.000***
-
-
-
-0.412*** -0.000 0.1089
7 0.340*** -0.006***
-
-
0.000***
-
-
-0.572*** -0.000 0.111
8 0.335*** -0.005***
-
-
-
0.006***
-
-0.631*** -0.000 0.120
9 0.338*** -0.006***
-
-
-
-
0.006*** -0.627*** -0.000 0.118
Δ
UST10Y
4 0.297*** -0.006***
-
-
-
-
-
-
-0.000 0.089
5 0.290*** -0.005*** 0.003***
-
-
-
-
-0.502*** -0.001 0.098
6 0.294*** -0.006***
-
-0.000**
-
-
-
-0.318*** -0.000 0.092
7 0.292*** -0.005***
-
-
0.000***
-
-
-0.462*** -0.001 0.095
8 0.287*** -0.005***
-
-
-
0.006***
-
-0.529*** -0.001 0.107
9 0.290*** -0.005***
-
-
-
-
0.006*** -0.523*** -0.000 0.104
Δ
UST30Y
4 0.203*** -0.005***
-
-
-
-
-
-
-0.000 0.058
5 0.199*** -0.004*** 0.003***
-
-
-
-
-0.195** -0.001 0.066
6 0.203*** -0.005***
-
-0.000**
-
-
-
-0.010*** -0.000 0.059
7 0.201*** -0.004***
-
-
0.000***
-
-
-0.152** -0.001 0.062
8 0.195*** -0.004***
-
-
-
0.007***
-
-0.237*** -0.001 0.080
9 0.198*** -0.004***
-
-
-
-
0.006*** -0.218*** -0.000 0.073
Note:
*** and ** represent statistical significance at the 1 percent and 5 percent level, respectively.
19
Table 5: Robustness Tests (with
Δ
VIX)
Eq. 4
Eq. 5
Eq. 6
Eq. 7
Eq. 8
Eq. 9
Breusch-Godfrey serial correlation LM Test
Δ
UST2Y
0.000 0.454 0.332 0.466 0.428 0.447
Δ
UST3Y
1.022 0.082 0.147 0.071 0.093 0.068
Δ
UST5Y
1.996 0.690 0.823 0.558 0.616 0.581
Δ
UST7Y
3.322 1.796 1.933 1.410 1.576 1.497
Δ
UST10Y
4.882** 3.273 3.626 2.648 2.964 2.857
Δ
UST30Y
0.675 0.270 0.551 0.093 0.094 0.095
Harvey heteroskedasticity test
Δ
UST2Y
2.428 1.900 2.381** 1.740 2.261 2.446
Δ
UST3Y
2.063 2.654** 1.464 2.422** 1.657 1.642
Δ
UST5Y
5.134*** 2.946*** 2.174 2.793** 2.435** 2.650**
Δ
UST7Y
1.521 1.355 1.408 1.382 1.469 1.208
Δ
UST10Y
1.075 1.591 2.483**
2.521** 2.110 2.328
Δ
UST30Y
2.336 3.032** 2.283 2.798** 2.927** 2.295
Note:
*** and ** represent statistical significance at the 1 percent and 5 percent level, respectively
20
In the next set of equations (i.e., [10] to [15]),
Δ
VIX is replaced by
Δ
VXN. Results from these
regressions, displayed in table 6, are very similar to what were found earlier. As before,
Δ
TB3M
has the strongest influence on the daily changes in Treasury yields. The magnitude of the
coefficient of
Δ
TB3M lies between 0.1 and 0.4. The coefficient on
Δ
VXN is always negative and
statistically significant at the 1 percent level. Coefficients for the daily change in commodities,
copper, and oil are positive and significant, while the coefficient of the daily changes in the gold
price is negative and significant in most equations. Finally, the coefficient of the daily change in
the dollar exchange rate is negative and significant in all but five equations. Robustness tests,
shown in table 7, suggest that there is no evidence of serial correlation (at least at the 5 percent
level) in any equation, though heteroskedasticity is sometimes present.
21
Table 6: Ordinary Least Squares Results (with
Δ
VXN) (time period: 12/18/1995–12/31/2018)
Eq.
Δ
TB3M
Δ
VXN
Δ
CRB
Δ
GOLD
Δ
COPPER
Δ
OIL1
Δ
OIL2
Δ
DOLLAR
Const R
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