Table 3 Estimated coefficient matrix of...

Table 3

Estimated coefficient matrix of VAR

(a) MP indicator: changes in the effective FFR
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ$ eFFR
excessR(−1) [t-stat]	0.1013 [1.5816]	−0.1403 [−3.2977]	0.0087 [2.2110]	0.0061 [1.1685]	−0.0107 [−10.5988]	0.0078 [2.0098]	0.0043 [0.6156]
realR(−1) [t-stat]	−0.0600 [−0.7045]	0.4605 [8.1411]	−0.0028 [−0.5339]	−0.0111 [−1.5945]	0.0007 [0.5063]	−0.0021 [−0.4009]	−0.0010 [−0.1091]
$Δ$ Tbill(−1) [t-stat]	−1.0943 [−0.9385]	−0.5663 [−0.7308]	−0.1623 [−2.2553]	0.0964 [1.0125]	0.0140 [0.7617]	−0.1074 [−1.5246]	−0.0575 [−0.4551]
termS(−1) [t-stat]	−0.2592 [−0.9552]	−0.4626 [−2.5646]	0.0584 [3.4837]	0.9107 [41.1080]	0.0080 [1.8606]	0.0736 [4.4882]	0.0525 [1.7851]
dp(−1) [t-stat]	1.1658 [2.1697]	0.5676 [1.5894]	−0.0421 [−1.2702]	0.0568 [1.2960]	0.9699 [114.1160]	−0.0500 [−1.5395]	−0.0032 [−0.0545]
r.bill(−1) [t-stat]	0.4448 [1.0224]	0.2119 [0.7330]	0.1206 [4.4915]	−0.1463 [−4.1183]	0.0006 [0.0939]	0.9805 [37.2906]	0.2392 [5.0784]
$Δ$ eFFR(−1) [t-stat]	0.6203 [1.2049]	−0.1526 [−0.4459]	0.0234 [0.7353]	0.0169 [0.4015]	−0.0180 [−2.2133]	0.0251 [0.8081]	−0.4963 [−8.9033]
Adjusted R²	0.0409	0.3236	0.1245	0.9280	0.9871	0.8955	0.2898
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

(a) MP indicator: changes in the effective FFR
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ$ eFFR
excessR(−1) [t-stat]	0.1013 [1.5816]	−0.1403 [−3.2977]	0.0087 [2.2110]	0.0061 [1.1685]	−0.0107 [−10.5988]	0.0078 [2.0098]	0.0043 [0.6156]
realR(−1) [t-stat]	−0.0600 [−0.7045]	0.4605 [8.1411]	−0.0028 [−0.5339]	−0.0111 [−1.5945]	0.0007 [0.5063]	−0.0021 [−0.4009]	−0.0010 [−0.1091]
$Δ$ Tbill(−1) [t-stat]	−1.0943 [−0.9385]	−0.5663 [−0.7308]	−0.1623 [−2.2553]	0.0964 [1.0125]	0.0140 [0.7617]	−0.1074 [−1.5246]	−0.0575 [−0.4551]
termS(−1) [t-stat]	−0.2592 [−0.9552]	−0.4626 [−2.5646]	0.0584 [3.4837]	0.9107 [41.1080]	0.0080 [1.8606]	0.0736 [4.4882]	0.0525 [1.7851]
dp(−1) [t-stat]	1.1658 [2.1697]	0.5676 [1.5894]	−0.0421 [−1.2702]	0.0568 [1.2960]	0.9699 [114.1160]	−0.0500 [−1.5395]	−0.0032 [−0.0545]
r.bill(−1) [t-stat]	0.4448 [1.0224]	0.2119 [0.7330]	0.1206 [4.4915]	−0.1463 [−4.1183]	0.0006 [0.0939]	0.9805 [37.2906]	0.2392 [5.0784]
$Δ$ eFFR(−1) [t-stat]	0.6203 [1.2049]	−0.1526 [−0.4459]	0.0234 [0.7353]	0.0169 [0.4015]	−0.0180 [−2.2133]	0.0251 [0.8081]	−0.4963 [−8.9033]
Adjusted R²	0.0409	0.3236	0.1245	0.9280	0.9871	0.8955	0.2898
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

(b) MP indicator: changes in the shadow FFR by Wu and Xia (2016)
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ$ WX
excessR(−1) [t-stat]	0.0886 [1.3769]	−0.1474 [−3.4708]	0.009 [2.2822]	0.0061 [1.1554]	−0.0103 [−10.0549]	0.0082 [2.123]	0.0009 [0.402]
realR(−1) [t-stat]	−0.0767 [−0.9028]	0.4548 [8.109]	−0.0027 [−0.5178]	−0.0113 [−1.627]	0.0012 [0.9137]	−0.0018 [−0.3596]	0.003 [1.0815]
$Δ$ Tbill(−1) [t-stat]	−0.8862 [−0.7632]	−0.5327 [−0.6951]	−0.1608 [−2.2534]	0.0996 [1.0539]	0.0074 [0.4018]	−0.1068 [−1.5312]	0.0974 [2.5345]
termS(−1) [t-stat]	−0.2586 [−0.9408]	−0.4232 [−2.3325]	0.0554 [3.2809]	0.9096 [40.6473]	0.0077 [1.7603]	0.07 [4.2373]	0.0328 [3.6102]
dp(−1) [t-stat]	1.1792 [2.1861]	0.5349 [1.5024]	−0.0394 [−1.1893]	0.058 [1.3218]	0.9697 [112.9883]	−0.0467 [−1.4419]	−0.03 [−1.679]
r.bill(−1) [t-stat]	0.5825 [1.0251]	0.5533 [1.4753]	0.0977 [2.7988]	−0.1532 [−3.3113]	−0.0059 [−0.6544]	0.9514 [27.8652]	0.1238 [6.5867]
$Δ$ WX(−1) [t-stat]	−0.3661 [−0.1785]	−1.9962 [−1.4746]	0.1423 [1.1287]	0.0493 [0.2953]	0.0249 [0.7625]	0.178 [1.4447]	0.1599 [2.3564]
Adjusted R²	0.0353	0.3290	0.1271	0.9279	0.9869	0.8961	0.4797
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

(b) MP indicator: changes in the shadow FFR by Wu and Xia (2016)
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ$ WX
excessR(−1) [t-stat]	0.0886 [1.3769]	−0.1474 [−3.4708]	0.009 [2.2822]	0.0061 [1.1554]	−0.0103 [−10.0549]	0.0082 [2.123]	0.0009 [0.402]
realR(−1) [t-stat]	−0.0767 [−0.9028]	0.4548 [8.109]	−0.0027 [−0.5178]	−0.0113 [−1.627]	0.0012 [0.9137]	−0.0018 [−0.3596]	0.003 [1.0815]
$Δ$ Tbill(−1) [t-stat]	−0.8862 [−0.7632]	−0.5327 [−0.6951]	−0.1608 [−2.2534]	0.0996 [1.0539]	0.0074 [0.4018]	−0.1068 [−1.5312]	0.0974 [2.5345]
termS(−1) [t-stat]	−0.2586 [−0.9408]	−0.4232 [−2.3325]	0.0554 [3.2809]	0.9096 [40.6473]	0.0077 [1.7603]	0.07 [4.2373]	0.0328 [3.6102]
dp(−1) [t-stat]	1.1792 [2.1861]	0.5349 [1.5024]	−0.0394 [−1.1893]	0.058 [1.3218]	0.9697 [112.9883]	−0.0467 [−1.4419]	−0.03 [−1.679]
r.bill(−1) [t-stat]	0.5825 [1.0251]	0.5533 [1.4753]	0.0977 [2.7988]	−0.1532 [−3.3113]	−0.0059 [−0.6544]	0.9514 [27.8652]	0.1238 [6.5867]
$Δ$ WX(−1) [t-stat]	−0.3661 [−0.1785]	−1.9962 [−1.4746]	0.1423 [1.1287]	0.0493 [0.2953]	0.0249 [0.7625]	0.178 [1.4447]	0.1599 [2.3564]
Adjusted R²	0.0353	0.3290	0.1271	0.9279	0.9869	0.8961	0.4797
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

(c) MP indicator: changes in the shadow FFR by Krippner (2013)
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ KR$
excessR(−1) [t-stat]	0.0847 [1.3097]	−0.136 [−3.172]	0.0062 [1.591]	0.0061 [1.1533]	−0.0106 [−10.2874]	0.0053 [1.3722]	0.0174 [3.361]
realR(−1) [t-stat]	−0.0737 [−0.873]	0.4638 [8.2828]	−0.0029 [−0.5666]	−0.0115 [−1.6789]	0.0012 [0.8605]	−0.0022 [−0.4401]	−0.0152 [−2.2455]
$Δ$ Tbill(−1) [t-stat]	−1.0364 [−0.8695]	−0.5755 [−0.728]	−0.2045 [−2.8305]	0.1078 [1.1107]	0.0045 [0.2372]	−0.1486 [−2.1007]	0.0188 [0.1969]
termS(−1) [t-stat]	−0.2866 [−1.0399]	−0.4551 [−2.49]	0.0504 [3.0183]	0.9115 [40.6133]	0.0076 [1.7238]	0.0657 [4.0197]	−0.0004 [−0.0175]
dp(−1) [t-stat]	1.2127 [2.2388]	0.555 [1.5448]	−0.031 [−0.9454]	0.0561 [1.2705]	0.9702 [112.5621]	−0.039 [−1.212]	0.0097 [0.2241]
r.bill(−1) [t-stat]	0.4848 [1.1091]	0.2033 [0.7012]	0.1117 [4.2146]	−0.1429 [−4.0123]	−0.0024 [−0.3402]	0.9719 [37.4613]	0.0488 [1.3953]
$Δ$ KR(−1) [t-stat]	0.3977 [0.4769]	−0.1127 [−0.2039]	0.1455 [2.8781]	−0.0182 [−0.2683]	0.0116 [0.8718]	0.144 [2.91]	0.1489 [2.231]
Adjusted R²	0.0361	0.3232	0.1513	0.9279	0.9869	0.8987	0.1330
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

(c) MP indicator: changes in the shadow FFR by Krippner (2013)
	excessR	realR	$Δ T$ Bill	termS	dp	r.bill	$Δ KR$
excessR(−1) [t-stat]	0.0847 [1.3097]	−0.136 [−3.172]	0.0062 [1.591]	0.0061 [1.1533]	−0.0106 [−10.2874]	0.0053 [1.3722]	0.0174 [3.361]
realR(−1) [t-stat]	−0.0737 [−0.873]	0.4638 [8.2828]	−0.0029 [−0.5666]	−0.0115 [−1.6789]	0.0012 [0.8605]	−0.0022 [−0.4401]	−0.0152 [−2.2455]
$Δ$ Tbill(−1) [t-stat]	−1.0364 [−0.8695]	−0.5755 [−0.728]	−0.2045 [−2.8305]	0.1078 [1.1107]	0.0045 [0.2372]	−0.1486 [−2.1007]	0.0188 [0.1969]
termS(−1) [t-stat]	−0.2866 [−1.0399]	−0.4551 [−2.49]	0.0504 [3.0183]	0.9115 [40.6133]	0.0076 [1.7238]	0.0657 [4.0197]	−0.0004 [−0.0175]
dp(−1) [t-stat]	1.2127 [2.2388]	0.555 [1.5448]	−0.031 [−0.9454]	0.0561 [1.2705]	0.9702 [112.5621]	−0.039 [−1.212]	0.0097 [0.2241]
r.bill(−1) [t-stat]	0.4848 [1.1091]	0.2033 [0.7012]	0.1117 [4.2146]	−0.1429 [−4.0123]	−0.0024 [−0.3402]	0.9719 [37.4613]	0.0488 [1.3953]
$Δ$ KR(−1) [t-stat]	0.3977 [0.4769]	−0.1127 [−0.2039]	0.1455 [2.8781]	−0.0182 [−0.2683]	0.0116 [0.8718]	0.144 [2.91]	0.1489 [2.231]
Adjusted R²	0.0361	0.3232	0.1513	0.9279	0.9869	0.8987	0.1330
Adjusted R² without MP indicator	0.0352	0.3230	0.1226	0.9279	0.9868	0.8952	N.A.

Note(s): The table reports estimated coefficient matrix, $A$ ⁠, in equation (4). The state variables are CRSP equity excess return (excessR), real rate of interest (realR), treasury-bill rate changes (⁠ $Δ Tbill)$ ⁠, dividend–price ratio (dp), term spread between the ten-year and one-month treasury yields (termS), and relative bill rate (r.bill). Here, the change in effective FFR (∆eFFR) is applied as the seventh state variable in Panel (a); Panel (b) applies the change in the shadow rate from Wu and Xia (2016, ∆WX), and Panel (c) the change in the shadow rate from Krippner (2013, ∆KR). The second to the last row shows adjusted R² for each equation in the VAR system. We also estimated the VAR without the seventh variable, MP indicator, of which the adjusted R² for each equation are reported in the last row (adjusted R² without MP indicator), N.A. – not available

[ViewLarge]

Sharing Unavailable