2016 1 12 4
1 2016 1 12, 1), 2) (Markov-Switching Vector Autoregression, MSVAR), 3) 3, 1980 1990.,, 225 1986 4 1990 6, TOPIX,1986 5 1990 2, explosive. 2,.,,,.,, 1986 Q2 1990 Q2,,. :, explosive, recursiveadf, MSVAR, 4
1 1.1,, 1980 1990., 1), 2) (Markov-Switching Vector Autoregression, MSVAR), 3). 1980 1990,., 1985.,.,,,,.,, 38957.44 1).,,.,, ( 1 ). 90,,,.,.,,,,.,,., 1987,. 1990., 2),.,, 2000,,,, 3., Phillips et al.(2012), AR(1). AR(1),.. x t = µ x + δx t 1 + ε t,x (1.1) δ > 1,, explosivear(1)., 0 < δ < 1, AR(1), δ = 1,.,,,.,, explosive. 1) 1989 12 29 2), 2
1.2, (2009) Phillips et al.(2012), recursiveadf, 225 TOPIX. 10000 35000 1985 1990 1995 2000 2005 2010 2015 1000 2500 1985 1990 1995 2000 2005 2010 2015 20 50 1985 1990 1995 2000 2005 2010 2015 1: 225( ), TOPIX( ), ( /m 2 ). 1.2,, FRB view BIS view 2 3). FRB view.,,.,,.,,., BIS View,..,,, 3) (2008) 3
1.2.,,.,.,., 1), 2), 3).,,,.,,MSVAR,.,,.,,.,,.. 目的 手段 バブル期間の推定 単位根検定 バブル構造変化の推定 MSVAR バブル期間のみ株価に影響を与える変数の存在 インパルス応答関数 2:.,,,,.,.. 2,,, MSVAR. 3, 4
recursive ADF. 4, MSVAR,,. 5,., 6. 2, MSVAR.,. (2007),,,,,. (2000),,,, 4. (2000),,,,.,,,., 5,., (2012, 2013),, 2,,,.,, (2008) (Dynamic General Equilibrium, DGE),.,,., 1980 90,. MSVAR, Hamilton(1989)., Krolzig(1998) Ox MSVAR.,. Fujiwara(2004) MSVAR,,,,., Inoue and Okimoto(2007) MSVAR, 1996. 5
3, recursiveadf. recursiveadf,,,, MSVAR. 3.1, (2009) Phillips et al.(2012),., t D t, t P t, t E t., R( ). P t = 1 1 + R E t(p t+1 + D t+1 ) (3.1) Campbell and Shiller(1989),. p t = p f t + b t (3.2) p f t = κ γ 1 ρ + (1 ρ) ρ i E t p t+i (3.3) i=0 b t = lim i ρ i E t p t+i (3.4) E t (b t+1 ) = 1 ρ b t = (1 + exp(d p)b t ) (3.5) κ = log(ρ) (1 ρ) log( 1 1) (3.6) ρ, p t = log(p t ), d t = log(d t ), γ = log(1 + R)ρ = 1/(1 + exp(d p)), d p = E[log(D t /P t )]. p f t,,. b t,,. b t = 1 ρ b t 1 + ε b,t (1 + g)b t 1 + ε b,t, E t 1 (ε b,t ) = 0 (3.7) g = 1 ρ 1 = exp(d p) > 0,., ε b,t, b t.,(2) b t 0., (3.2), b t = 0,, p t = p f t = µ + (1 ρ) ρ i E t (d t+1+i ), 0 < ρ < 1 (3.8) i=0 6
3.2 ADF, d t p t., d t p t. d t p t = κ γ 1 ρ ρ i E t ( d t+1+i ) (3.9), d t I(0), p t d t (1, 1)., = 1 L, L., b t 0,, (3.7) b t explosive, (3.2), p t explosive., b t p t., d t I(1) I(0), p t explosive,., p t d t.,, p t explosive 4).,, explosive. i=0 3.2 ADF,, Augumented Dickey-Fuller(ADF). t x t,. x t = µ x + δx t + J ϕ j x t j + ε x,t (3.10) j=1, J. I(1), δ = 1, I(0), δ < 1, explosivear, δ > 1. δ t ADF. ADF = t δ=1 = ˆδ 1 ˆσ δ (3.11). ˆσ δ, ˆδ. H 0, δ 1, H 1, δ > 1 5). 3.3 sup ADF, ADF, ADF Evans(1991).,, sup ADF. sup ADF. sup ADF = sup ADF [nr] (3.12) r [r 0,1] 4) d t I(1),. (2009) TOPIX, I(1). 5), δ = 1, δ < 1,. 7
3.4 recursiveadf, [ ], ADF [nr], 1 [nr] ADF., r 0., n = 500, r 0 = 0.1, sup ADF [nr] = max{adf 50, ADF 51, ADF 52,..., ADF 500 } (3.13) r [r 0,1] [nr 0 ] = 50, ADF 50 1, ADF,. ADF,,.,, (explosive),,, I(1)., sup ADF,,., ADF, sup ADF,. 3.4 recursiveadf, recursiveadf. n 0 n 1 ADF ADF (n 0, n 1 )., 1 n 0 < n 1 n. n. inf ADF (r) = sup ADF (r) = min ADF (1, k) (3.14) k [nr],...,n max ADF (1, k) (3.15) k [nr],...,n rangeadf (r) = sup ADF (r) inf ADF (r) (3.16) inf ADF, sup ADF., rangeadf, sup ADF inf ADF,. (2009),, sup ADF, ( )., TOPIX( ), 1986 3 1990 2.,TOPIX, 2,. (2009) Phillips et al(2012), recursiveadf, k [nr] + 1 k ADF rollingadf.,,, recursiveadf 6). 6) Phillips et al(2012), recursiveadf,,. 8
4 MSVAR, MSVAR 7). recursiceadf,, 2. 4.1 MSVAR,, K MSVAR(p). y t = Φ (1) 1 (s t)y t 1 + Φ (2) 2 (s t)y t 2 + + Φ (p) p (s t )y t p + ε t (4.1) s t = j j = 1,, K (4.2) y t,, s t 1 K. s t, s t s t., i j p ij, P (s t = j s t 1 = i, s t 2 = k,...) = P (s t = j s t 1 = i) = p ij., E(ε t ε t) = Ω(s t )., K P. p 11 p 21 p M1 p 12 p 22 p M2 P =...... p 1M p 2M p MM M p ij = 1, i, j (1, M) (4.3) P (j, i), p ij. (2, 1), 1 2., 3 3 MSVAR(2). j=1 y 1,t y 2,t = + ϕ (1) 11 ϕ (1) 12 ϕ (1) 13 ϕ (1) 21 ϕ (1) 22 ϕ (1) 23 (s t ) y 3,t ϕ (1) 31 ϕ (1) 32 ϕ (1) 33 ϕ (2) 11 ϕ (2) 12 ϕ (2) 13 ϕ (2) 21 ϕ (2) 22 ϕ (2) 23 (s t ) y 1,t 2 y 2,t 2 ϕ (2) 31 ϕ (2) 32 ϕ (2) y 3,t 2 33 p 11 p 21 p 31 s t = [1, 2, 3] P = p 12 p 22 p 32 p 13 p 23 p 33 y 1,t 1 y 2,t 1 (4.4) y 3,t 1 + ε 1 ε 2 (4.5) ε 3 3 p ij = 1 (4.6), 1. j=1 7) VAR (2010) 9
4.2,. P = p 11 0 0 1 p 11 p 22 0 (4.7) 0 1 p 22 p 33, 1 2 3., p 11, p 22, p 33, P.,,, MSVAR. 4.2,.,. ξ k ij(h) = E ty t+h ε jt st = =s t+h =k (4.8), k y t, 1 (h k )h. MSVAR,,.,,.,. 4.3 MSVAR., EM (Gibbs sampler), 8)., R MSBVAR., Patrick(2015), MSVAR., MSBVAR,, Inoue and Okimoto(2007)., MSVAR. θ = [θ 1, θ 2, θ 3, θ 4] (4.9) θ 1 = [s 1, s 2,, s T ] (4.10) θ 2 = [p 11, p 12, p 21, p 22,, p MM ] (4.11) θ 3 = [vech(ω(1)), vech(ω(2)),, vech(ω(k)) ] (4.12) θ 4 = [β(1), β(2),, β(n) ] (4.13) β(j) = [vec(φ (1) 1 (j)), vec(φ (2) 2 (j)),, vec(φ (p) p (j)) ] (4.14) 8), (2007) 10
4.3 vech( ), vec( ).. 1 2 3 vech 4 5 6 = ( 1 2 3 5 6 9 ) (4.15) 7 8 9 1 ( ) 2 1 3 5 vec = 3 2 4 6 4 (4.16) 5 6 6, p(θ ŷ T ) 9), θ (0), j = 0 N. 1) θ (j+1) 1 p(θ 1 θ (j) 2, θ(j) 3, θ(j) 4, ŷ T ) ( ), Baum-Hamilton-Lee-Kim(BHLK) filter and smoother., forward-filter-backward-sample. 2) θ (j+1) 2 p(θ 2 θ (j) 1, θ(j) 3, θ(j) 4, ŷ T ) ( ) Dirichlet. 3),,. 4) θ (j+1) 3 p(θ 3 θ (j) 1, θ(j) 2, θ(j) 4, ŷ T ) ( ). 5) θ (j+1) 4 p(θ 4 θ (j) 1, θ(j) 2, θ(j) 3, ŷ T ) ( ). 6) j + 1 = N.,. MSVAR, EM,,,. MSVAR,,,,., EM 9) ŷ T = {y p+1, y p+2,, y t }. 11
.,, (MCMC). MCMC,,.,,,.. 5,, ADF MSVAR. ADF,. MSVAR, ADF,. 5.1 3 ADF, 225 TOPIX., 1970 1 2014 12. (CPI), ( 3 ). r 0 = 0.1, 1974 6 ADF. 4.0 4.5 5.0 5.5 6.0 1970 1980 1990 2000 2010 1.5 2.0 2.5 3.0 3.5 1970 1980 1990 2000 2010 3: 225 TOPIX 225, TOPIX. 1974 6 ADF 4. 0 12
5.1 5%., 225 1986 4, 1990 6. TOPIX, 1986 5, 1990 2,, 1987 10 19., 1,, AR(1) 1, explosivear(1) 10). 3, recursiveadf. supadf,, explosive. 2.0 1.0 0.0 0.5 1.0 1.5 1986/4 1990/6 1980 1990 2000 2010 2.0 1.0 0.0 0.5 1.0 1986/5 1990/2 1980 1990 2000 2010 4: 225 TOPIX recursive ADF 225, TOPIX. (1970 1 ) 1985 10 1986 4 1987 7 1990 6 1990 12 0.9884 1.0020 1.0152 1.0024 0.9971 (1970 1 ) 1985 10 1986 5 1987 3 1990 2 1990 12 0.9997 1.0123 1.0241 1.0048 0.9989 1: AR(1) (x t = µ x + δx t 1 + ε x,t ) δ ( 225, TOPIX) 10) AR(1), 2. 13
5.1 supadf (r) infadf (r) rangeadf (r) (r 0 = 1/10) 1.4001 1.8881 3.2882 supadf (r) infadf (r) rangeadf (r) (r 0 = 1/10) 1.3094 2.1724 3.4818 2: recursiveadf ( 225, TOPIX),. sup ADF, 225 TOPIX explosive. 225 explosive, 1986 4 1990 6. TOPIX explosive, 1986 5 1990 2. 1970 1 explosive AR(1), δ 1.,.1, 225 TOPIX., 225 1986 4, TOPIX 1986 5 1.,, 225 1990 6, TOPIX 1990 2 4., 225 TOPIX. 225, 225, TOPIX., TOPIX,, TOPIX, 225., 225 TOPIX 11), TOPIX 225, TOPIX 225 12). 2,TOPIX, (2009). (2009) explosive, 1986 3 1990 2., 2., (2009) (1970 1 2003 4 ),. 3, (2000 IT 2007 ).,,. 1970 1,, 11) 10 AIC 2 VAR(6)., (2010). 12), 225 TOPIX. 14
5.2 MSVAR, explosive,.,,,. 5.2 MSVAR, 4 MSVAR. 5.2.1 MSVAR,. MSVAR, (2010). (2010),, 1985, 86, 87,.,,.,, 225,,,, (CPI) 5.,, 2 13).,,,., 2 5 MSVAR (1)., 1980Q1 2014Q4.,,,,. 5, Nikkei-E-I-Oil-CPI., MSVAR, burn-in 1000, 10000. E 5 0 5 CPI 1 0 1 2 3 Nikkei 20 10 0 10 20 Oil 40 20 0 20 I 1980 1985 1990 1995 2000 2005 2010 2015 10 5 0 5 10 Time 1980 1985 1990 1995 2000 2005 2010 2015 Time 5:. 13) 3, 2. 15
5.2 MSVAR 5.2.2 MSVAR 14). 6, 2., 1 1990 Q1 Q2 2008 Q2 Q3.,. 1990 Q1 Q2, 225 1986 4 (=Q2) 1990 6 (=Q2),., 2008 Q2 Q3,.,. 2008 9 15 (=Q3), 1., 2008 9 12 12214, 1 10 28, 6994., 1, 225 explosive,,.,, 1,,., 7., 12. 4. 1, 1 2 225 (I Nikkei).,,,.,. 2, 1 2, (Nikkei Nikkei, I I).,,, 2. 3, (Nikkei I, Nikkei CPI).,,. 4, 1, (Oil I)., 1,.,. 1,.,,,,. 14) MSVAR.B 16
5.2 MSVAR 0.0 0.2 0.4 0.6 0.8 1.0 state1 state2 1980 1985 1990 1995 2000 2005 2010 2015 6: (x, y ). 7: 1 ( 95% ). 17
5.2 MSVAR 8: 2 ( 95% ). Nikkei Nikkei 0 5 10 20 E 0 2 4 6 6 2 2 6 I Shock to E I Oil CPI Oil 0 10 20 30 CPI 15 5 5 0 2 4 6 0 5 10 20 6 2 2 6 0 10 20 30 15 5 5 0 2 4 6 0 5 10 20 6 2 2 6 0 10 20 30 15 5 5 0 5 10 20 6 2 2 6 0 2 4 6 15 5 5 0 10 20 30 0 5 10 20 6 2 2 6 0 2 4 6 15 5 5 0 10 20 30 Response in 9: 1,2 ( 95% ).,. 18
5.3 (, ).,.,.,.,. 1,,. 225. 5, 225.,, 225 15). 2,. 1990 2000 IT,,., 225.,.,, 16)., 5,,.,,,, 225. 5.3 2,.,,. 5.3.1,. 15) MSVAR,. 16) 1990,,,. 19
5.3 y t = β 0 + (β 1 + β 2 D 1 (t))rate t d + ε t (5.1) y t = β 0 + (β 1 + β 3 D 2 (t))rate t d + ε t (5.2) y t = β 0 + (β 1 + β 2 D 1 (t) + β 3 D 2 (t))rate t d + ε t (5.3) y t = β 0 + (β 1 + β 2 D 1 (t))rate t d + β 4 ST t + β 5 EX t + β 6 MB t + ε t (5.4) { 0 (t S k ) D 1 (t) = t + 1 t 0 (t S k ), D 2(t) = t t = 1,., 175 (5.5) { {1986Q1,, 1990Q2} ( ) S k = (5.6) {1986Q1,, 1990Q1} (TOPIX ) y t 225 or TOPIX( ) Rate t ST t TOPIX or 225( ) EX t MB t D 1 (t) D 2 (t), 4., 225 TOPIX 2., (5.1), ( 1), (5.2), ( 2), (5.3), 1 2 ( 3), (5, 4), (5.1), ( 225, TOPIX ),, ( 4). D 1 (t), S k 1, 2, 3, 1, 0.,, 225, 1986 Q1 1990 Q2, TOPIX, 1986 Q1 1990 Q1., D 2 (t), 1, 2, 3, 1., 1970 Q1 2014 Q4.,, β 2,. 1,,, 2,., 3 4, β 2,., 5. I) (d = 0), II) 1 (d = 1), III) 1, IV) 1, V) D j (t) = k, j = 1, 2 k k 2 5. 5 20
5.3, I), II)1, III, IV), V), (4 ) (5 ) (2 ) (2 ) 80. 3.., I II, III, IV, V. Nikkei225 TOPIX / 1 2 3 4 1 2 3 4 I n 1 I N n 2 I N n 3 I N n 4 I N n 1 I T n 2 I T n 3 I T n 4 I T n t 1 I N t 2 I N t 3 I N t 4 I N t 1 I T t 2 I T t 3 I T t 4 I T t II n 1 II N n 2 II N n 3 II N n 4 II N n 1 II T n 2 II T n 3 II T n 4 II T n t 1 II N t 2 II N t 3 II N t 4 II N t 1 II T t 2 II T t 3 II T t 4 II T t III n 1 III N n 2 III N n 3 III N n 4 III N n 1 III T n 2 III T n 3 III T n 4 III T n t 1 III N n 2 III N n 3 III N n 4 III N n 1 III T n 2 III T n 3 III T n 4 III T n IV n 1 IV N n 2 IV N n 3 IV N n 4 IV N n 1 IV T n 2 IV T n 3 IV T n 4 IV T n t 1 IV N t 2 IV N t 3 IV N t 4 IV N t 1 IV T t 2 IV T t 3 IV T t 4 IV T t V n 1 V N n 2 V N n 3 V N n 4 V N n 1 V T n 2 V T n 3 V T n 4 V T n t 1 V N t 2 V N t 3 V N t 4 V N t 1 V T t 2 V T t 3 V T t 4 V T t 3: (n, t TOPIX.),,,,.,,.,,,.,, 17). 17), 21
5.3 Excange.Rate 5 0 5 Time.Dummy 0 50 100 150 O.N.Rate 1 0 1 2 Bubble.Dummy.T. 0 5 10 15 TOPIX 15 5 0 5 10 Bubble.Dummy.N. 0 5 10 15 Nikkei 15 5 0 5 10 Monetary.Base 6 2 2 6 1970 1980 1990 2000 2010 Time 1970 1980 1990 2000 2010 Time 10:. 5.3.2, β 2 β 3 10%, 4., I II, II., III V 1. 4, TOPIX 1 (= ), k 2., β 3 β 2 TOPIX, 1. Nikkei225 TOPIX 1 2 3 4 1 2 3 4 I n t II n t III n t IV n t V n t 4: ( 10% β 2, II β 3 ) 22
5.3 II n IV t 5., TOPIX 4,,.,., (, 1986 Q2 1990 Q2 ),., 4,,,., 6 V n., 5 t., k k 2,., R 2, 5 6, k 2.. (1986 Q2 1990 Q2), ( 225, TOPIX).,., k k 2, 18).,.,. 1, TOPIX,., 1986 4 (5.0% 3.0%) 19).,, 1989 5 31.,, 1986 Q2 1990 Q2, 1986 1989.,,,. 2,,.,.,,,.,, 18), k 3, k 2 t R 2. 19) 1 30 5.0% 4.5%, 3 10, 4.5% 4.0%, 4 21, 4.0% 3.5%, 11 1, 3.5% 3.0%,, 2 23, 3.0% 2.5%. 23
5.3. Nikkei225 TOPIX 1 2 3 4 1 2 3 4 β 0 0.600 0.434 0.661 0.201 0.576 0.464 0.625 0.266 ( ) (1.741) (1.237 ) (1.875 ) ( 1.108) (1.853 ) (1.478 ) (1.963 ) (1.621) β 1 0.322 0.745 1.088 0.234 0.624 0.994 1.237 0.316 ( ) ( 0.516) ( 0.657) ( 0.975) (0.874) ( 1.108) ( 0.979) ( 1.226) ( 1.271) β 2 0.436 0.481 0.127 0.315 0.341 0.040 ( ) ( 2.785 ) ( 2.901 ) ( 1.809 ) ( 2.155 ) ( 2.274 ) (0.620) β 3 0.002 0.002 0.001 0.014 ( ) ( 0.128) (0.828) ( 0.013) (0.733) β 4 0.990 0.815 ( ) (26.588 ) (26.588 ) β 5 0.006 0.480 ( ) ( 0.079) ( 0.700) β 6 0.231 0.175 ( ) (2.322 ) ( 1.930) R 2 0.043 0.001 0.042 0.812 0.034 0.008 0.032 0.814 5: II n IV t ( t,,,,, 0.1%, 1%, 5%, 10% ) Nikkei225 TOPIX 1 2 3 4 1 2 3 4 β 0 0.628 0.434 0.688 0.189 0.593 0.464 0.640 0.259 ( ) (1.822) (1.237 ) (1.948 ) ( 1.038) (1.901 ) (1.478 ) (2.002 ) (1.571) β 1 0.367 0.745 1.109 0.235 0.664 0.994 1.245 0.322 ( ) ( 0.596) ( 0.657) ( 0.995) (0.869) ( 1.193) ( 0.979) ( 1.235) ( 1.311) β 2 0.029 0.031 0.009 0.020 0.022 0.003 ( ) ( 2.909 ) ( 3.011 ) ( 2.024 ) ( 2.192 ) ( 2.296 ) (0.806) β 3 0.002 0.017 0.001 0.013 ( ) ( 0.128) (0.799) ( 0.013) (0.692) β 4 0.989 0.816 ( ) (26.609 ) (26.609 ) β 5 0.006 0.471 ( ) ( 0.076) ( 0.689) β 6 0.231 0.175 ( ) (2.330 ) ( 1.930 ) R 2 0.047 0.001 0.045 0.818 0.034 0.008 0.032 0.814 6: V n ( t,,,,, 0.1%, 1%, 5%, 10% ) 24
6, 3, 1980 90., TOPIX 1986 5 1990 2, 225 1986 4 1990 6, explosive., MSVAR,,,.,,,,.,, 1986 Q2 1990 Q2,., 2. 1,..,,. 2, ( ).,,,.,.,., 2012 12,,., 2012 11 9000, 2015 4 15 20000., 2010,,., 20).,.,,,.,.,. 1,.,. (2000), 1970 97,,.,,,. 2, MSVAR.,, 20) 2012 12, 200, 2015 8, 86. 25
.,.,,,., 21),,.,, MSVAR 22). [1] 2010 85-87 [2] 1980 2000 263-319 [3] 2010 74-188 [4] 2009 7 2009 1-25 [5] 2000 220-243 [6] 2012 83-86 [7] 2013 133-137 [8] 2008 33-47 [9] 2008 400-401 [10] 2007 174 [11] 120-153 [12] 81-117 [13] Campbell, J. Y., and Shiller R., The Dividend-Price Ratio and Expectation of Future Dividend and Discount Factors, Review of Financial Studies 1, 1989, 195-228 [14] Evans, George, W., Pitfalls in Testing for Explosive Bubbles in Asset Prices, Economic Review 81, 1991, pp. 922-930 [15] Fujiwara, Ippei, Evaluationg Monetary Policy When Nominal Interest Rates are Almost Zero, Research and Statistics Department, Bank of Japan, 2004, pp.1-24 21) (2000) 22),. 26
[16] Hamilton, James, A New Approach to the Economic Analysis of Nonstationary Time Series and the Buiness Cycle, Econometrica 57(2), 1989, pp. 357-384 [17] Inoue, Tomoo, Okimoto, Tatsuyoshi, Were There Structural Breaks in the Effect of Japanese Monetary Policy? Re-evaluating Policy Effects of the Lost Decade, Faculty of Economics and IG555, Yokohama National University, 2007, pp. 1-25 [18] Krolzig, Hans, M., Econometric Modelling of Markov-Switching Vector Autoregressions using MSVAR for Ox, Institute of Economics and Statistics and Nuffield College, Oxford, 1998, pp. 1-20 [19] Patrick, Brandt, Package MSBVAR, CRAN, 2015, pp.1-92 [20] Phillips, Peter, C. B., Wu, Yangru and Yu, Jun, Explosive Behavior in the 1990s Nasdaq : When Did Exuberance Escalate Asset Values?, Couwles Foundation Paper NO.1349, 2012, pp. 201-207 20 27
.A 225, TOPIX, NEEDS (CPI) 22 2010 =100 2005 =100 IMF 85 6, 7:.B MSVAR B.1 MSVAR Naive SR Time-Series SE p 11 0.8977 0.0297 0.0003 0.0003 p 12 0.1023 0.0297 0.0003 0.0003 p 21 0.0691 0.0290 0.0003 0.0005 p 22 0.9309 0.0290 0.0003 0.0005 8: MSVAR 28
B.2 MSVAR B.2 MSVAR Naive SR Time-Series SE Nikkei 0.2876 0.3567 0.0036 0.0049 Nikkei 0.9390 0.0788 0.0008 0.0014 E 0.1363 0.1827 0.0018 0.0026 I 0.1123 0.1457 0.0014 0.0019 Oil 0.0581 0.0569 0.0006 0.0008 CPI 0.5452 0.7461 0.0075 0.0100 E 0.0305 0.1388 0.0014 0.0016 Nikkei 0.0047 0.0133 0.0001 0.0001 E 0.8320 0.1692 0.0017 0.0032 I 0.0185 0.0401 0.0004 0.0005 Oil 0.0024 0.0095 0.0001 0.0001 CPI 0.0725 0.1865 0.0019 0.0021 I 0.0767 0.1761 0.0018 0.0024 Nikkei 0.0311 0.0241 0.0002 0.0004 E 0.0232 0.0497 0.0005 0.0006 I 0.9452 0.0689 0.0007 0.0012 Oil 0.0121 0.0123 0.0001 0.0002 CPI 0.0006 0.2319 0.0023 0.0025 Oil 0.1698 0.4900 0.0049 0.0064 Nikkei 0.0229 0.0578 0.0006 0.0007 E 0.0591 0.1127 0.0011 0.0013 I 0.1191 0.1457 0.0014 0.0018 Oil 0.5663 0.1573 0.0016 0.0030 CPI 0.7271 1.0582 0.0106 0.0165 CPI 0.0047 0.2227 0.0022 0.0022 Nikkei 0.0019 0.0202 0.0002 0.0002 E 0.0024 0.0763 0.0008 0.0008 I 0.0062 0.0477 0.0005 0.0005 Oil 0.0022 0.0179 0.0002 0.0002 CPI 0.9374 0.2843 0.0028 0.0028 9: 1 MSVAR 29
B.2 MSVAR Naive SR Time-Series SE Nikkei 0.4457 0.1594 0.0016 0.0019 Nikkei 0.8176 0.0486 0.0005 0.0007 E 0.4057 0.1364 0.0014 0.0016 I 0.0284 0.1012 0.0010 0.0011 Oil 0.0121 0.0431 0.0004 0.0005 CPI 0.4083 0.4060 0.0041 0.0045 E 0.0187 0.0939 0.0010 0.0010 Nikkei 0.0104 0.0096 0.0001 0.0001 E 0.5218 0.0994 0.0010 0.0013 I 0.080 0.0258 0.0002 0.0003 Oil 0.0107 0.0100 0.0001 0.0001 CPI 0.0681 0.1278 0.0010 0.0010 I 0.0733 0.1203 0.0012 0.0013 Nikkei 0.0620 0.0138 0.0001 0.0002 E 0.0268 0.0377 0.0004 0.0004 I 0.8418 0.0375 0.0004 0.0004 Oil 0.0219 0.0092 0.0001 0.0001 CPI 0.0578 0.1789 0.0018 0.0020 Oil 0.2207 0.2642 0.0026 0.0032 Nikkei 0.0062 0.0328 0.0003 0.0004 E 0.0069 0.0790 0.0008 0.0009 I 0.0638 0.0817 0.0009 0.0010 Oil 0.4932 0.1131 0.0011 0.0016 CPI 0.4402 0.5519 0.0026 0.0032 CPI 0.0201 0.2449 0.0024 0.0024 Nikkei 0.0017 0.0023 0.0002 0.0002 E 0.0081 0.0950 0.0009 0.0009 I 0.0102 0.0538 0.0005 0.0005 Oil 0.0001 0.0274 0.0003 0.0003 CPI 0.8842 0.2449 0.0024 0.0024 10: 2 MSVAR 30