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1
2
3 I II
4 ...32 F
5 (*) *
6 1 2 3 The Ricardian Equivalence Theorem Barro(1974)
7 1 1 2 y 0 y 1 t 0,t 1 Y 0 y 0 t 0 Y 1 y 1 t 1 i C Y1 C 0 Y i 1+ i C 0 C 1,11 uuc 0 C 1 12 C 0 C 1 11 A Y 0 y 0 t 0 Y 0 0 Y0 B * C0 B 0 A Y 1 A Y1 E * C1 1 1 i Y 1 y 1 t 1 i 11 A 11 i E C 0 *C 1 * C 0 *Y 0 C 0 * 1i Y 0 C 0 * Y1 C 1 *1i Y 0 C 0 * Y 1 τ 0 τ 1 Y 0 y 0 t 0 Y 1 y 1 t 1 Y 0 y 0 t 0 τ 0 Y 1 y 1 t 1 τ 1 C1 y t τ C 0 y 0 t 0 τ 0 1+ i 1 i 11
8 τ 0 1i τ 0 τ 0 τ 1 i τ 0 τ 1 11 EC 0 *C 1 * Y0y 0t 0Y1y 1t 1 Y0y 0t 0τ 0Y1y 1t 1τ 1 11 A A AB τ0ab τ1 A A11i E C 0 *C 1 * BB Y 0 C 0 * ABY 0 C 0 * τ 0 12 i D S S D S D S D
9 2 Barro Mutoh 1985 Barro1983 Mutoh1985 Samuelson1980 p.353 Samuelson a Modigliani1961 Modigliani1961 b2 i C 1 ˆ y 0 t 0 C1y 1t 1 i 0 ˆ
10 y C t 0 1 ŷ y a y 1 y 1 i 0 y 1 0 y 1 t1 ˆ g1 t 0 ˆ g i 0 1 i 0 ĝ 0 ĝ 1 15 ˆ g 0 ĝ 1 i 0 Gi 0 t 0 t 1 Gi 0 15 A ~ ~ t 0 t 1 15 ~ ~ R 0 Bt 0 R 0 t 1 1 i 0 R 0 15 B B 0 A R 0 R 0 ĝ 0 A B B 1 A 1i 0 R C 0 ˆ y 0 ˆ g 0 C1 ˆ y 1 ˆ g 1 1 i t 0 t 1 16 ~ ~ ~ A t 0 t 1 B t 0 ~ R 0 t 1 1i 0 R 0 A B 16 A B 16 ˆ y 1 ˆ g1 C 0f i 0 ˆ y 0 ˆ g 0 1 i0 1 i0 17 ˆ y 0ˆ y 0 * C 0 ()C 0 ()I (i 0 ) I (i 0 ) g ˆ * ˆ0 g 0 18 C 0 ˆ g 0 18 C 0 18 i 0 c
11 C 0 C 0 C 0 C 0 16 C 0 C 0 18 C 0 C 0 i 0 I * i
12 C0YgS C11i g S C0Y1i g S C11i 1ig S 2 T112 ii 12 jj 0 j 1 S 1 S g T Y i i g 2 1 1i 2 g T1i 2 g C1 C0 Y i 2 2 C1 T C0 Y i 1 i BB 1 AA (C,C ) (1 i ) 1 (1 i ) (C 1 2,C 1 ) 1 1 AA 2 BB
13 Barro1974 Barro Barro t u t t t u t VC 0 C 1 u t C 0 C 1 t VC 0 C t1 t t t t t 2 u t1 t a 2
14 Barro t t t1 t1 t1 t t1 t1 t L t t C1 1i S t e t1 Le 117 t t S t t1 e t1 t1 L t1 e t t t t 1 e t e t e t L 118 t1 L t1 t1 t1 0 C Y t1 S t1 L 119 C t1 1 1i S t1 e t e t1 120 t1 L t S t1 S t1 S t1 L 121 L t118 t1 121 S t1 e t S t1 e t t1 t t1 t 118 t
15 1 I Barro Barro Kurz
16 contingent market BernheiniBagwell 1985 Blanchard II t1 0 C Y t1 S t1 τy t1 119 τ S t1 e t is t1 e t τ C t1 1 1i1τS t1 e t e t C t1 t1 C1 t τy 1 i 1 τ e t i τ t e i i1τ Kotolikoff1984 Barro1974 III III
17 III Barro IV IV I IV
18 2 1 Feldstein1982Kormendi1983 SeaterMariano1985Miller Aschauer Feldstein1982 Feldstein C t 0 1 Y t 2 W t 3 SSW t 4 G t 5 T t 6 TR t 7 D t 21 C Y W SSW G T TR D Feldstein Fiscal Signal Feldstein 2 OLS 6 3 fiscal signal Feldstein Kormendi1983 Feldstein 2
19 Kormendi Feldstein Kormendi SeaterMariano 1985FeldsteinKormendi t BeveridgeNelson1981 GNP 1 SeaterMariano Miller1982seemingly unrelated regression Aschauer1985 C t C t1 θg t1 θ G u t 22 e t G t θ G C 22 G C t G G e t G C t Aschauer Aschauer e t e t 2 Seater1982 FT t1 α 1 α 2 YDα 3 FP t 1eFG t α 4 WO t α 5 i t efg t1 23 FT t1 t1 YD t t FP t t FG t t WO t t i t t 23e
20 e0 FT t1 FT t FP t FG t 1 e1 FG t FT t1 FG t1 23 FT t FP t FG t FP t1 0 1 YD t 2 FP t 3 FG t 4 WO t 5 i t 6 FG t1 24 e1 3 α 3 1e0 6 e10 e0 3 α 3 1e 2 α e11 Seater Seater Plosser1982 causality F BlinderStiglitz1983 ΔX ΔX ΔR ΔD α L b L c L X X e 25 25X GNP GNP GNP R D Δ αl blcl 23 cl bl BlinderStiglitz GNP GNP GNP GNP R D 3
21 Feldstein fiscal signal Kormendi 5 0 F F
22 3 I 1 1 c w y τ g A D i i A t1 w t ia t c t τ t A t 31 1i 1 T T A k t k1 T w k t k T A k1 t k k0 k0 k0 T 1 A t k k1 c k t k T τ k t k k0 k0 T k1 T c k t k T w t k k0 k0 k 1i A t A kt1 T T τ k t k k0 A kt1 T 0T c k tk = w k tk (1i )A t τt k k0 k0 k0 1 k w k tk w t ia t A t τ k tk 32 0 k 32 w k tk k1 w t ia t A t τ k tk k0 32 W t T t (1i )A t 33 W t k0 T t k0 w tk k k τ k tk G t 1i D t T t c k tk W t G t 1i A t D t k0 35
23 35 35 Uc 0 c 1 t0 1 γ c t θ t γ c t W t T t 1i A t W t T t C t W e t T e t 1i A t 37 e iw e t T e t 1i A t W e t w t w t1 w t T e t e Tt G e t 1i D t T e t g t g t1 D t 1 G Feldstein1982 Fiscal Expectation 34
24 H H H T e t e Tt F g Lg t 1iD t F τ Lτ t 38 F L τ H F τ L y t w t ia t D t c t yf w Lw t F g Lg t F τ Lτ t A t D t k0 w e k tk F w Lw t F τ L0 g t 0 G t g t
25 AD Feldstein b 1965 II 1983 I 1975 τ g dτ ssτss g g
26 No. CONST y w w 1 τ dτ ssτ ss g AD A D R (8.01) 2882 (4.37) 2845 (10.74) 2949 (1.99) 2873 (11.31) 4835 (2.76) 575 (0.34) 0.20 (4.33) 0.23 (3.51) 0.37 (10.11) 0.53 (3.69) 0.38 (10.08) 0.55 (3.97) 0.48 (4.45) 0.49 (8.65) 0.49 (7.56) 0.25 (4.96) 0.36 (3.17) 0.17 (3.11) 0.35 (3.07) 0.26 (2.80) 0.23 (9.75) 0.21 (10.51) 0.13 (2.40) 0.29 (6.66) 0.13 (5.26) 0.26 (5.66) 0.17 (4.32) 0.01 (0.13) 0.07 (1.34) 0.06 (0.25) 0.00 (0.00) 0.00 (0.05) 0.02 (0.25) 0.08 (1.33) 0.48 (1.59) 1.09 (5.41) 0.29 (2.90) 0.42 (6.06) 0.11 (1.18) 0.88 (5.10) 0.22 (3.15) 0.86 (5.21) 0.55 (3.75) 0.04 (1.84) 0.02 (1.40) 0.00 (0.15) D.W OLS CORC D.W. 2. t II1983 I 1965 II1975 I 1975 II1983 I No. CONST y w w 1 τ τ 1 g g 1 AD (7.73) 2514 (8.53) 2918 (2.21) 3858 (2.38) (5.69) 0.39 (10.79) 0.42 (3.19) 0.43 (3.29) 0.48 (9.30) 0.29 (5.32) 0.52 (4.54) 0.50 (4.24) 0.07 (1.37) 0.09 (1.56) 0.18 (2.74) 0.16 (2.51) 0.03 (0.44) 0.27 (1.08) 0.01 (0.14) 0.01 (0.13) 0.25 (3.45) 0.22 (1.70) 0.11 (1.21) 0.11 (1.24) 0.29 (3.15) 0.19 (1.86) 0.83 (5.40) 0.82 (5.32) 0.48 (3.73) 0.33 (2.34) 0.47 (2.46) 0.44 (2.29) 0.02 (1.00) R 2 D.W OLS OLS OLS OLS OLS CORC OLS OLS OLS OLS OLS
27 No. CONST y w w 1 τ τ 1 g g 1 AD (6.26) 3260 (8.14) 3233 (2.10) 5138 (2.84) 2638 (6.21) 3252 (4.21) 3066 (2.27) 4017 (2.43) 0.22 (3.99) 0.34 (7.89) 0.54 (3.71) 0.56 (3.97) 0.27 (5.11) 0.34 (6.02) 0.42 (3.19) 0.44 (3.28) 0.44 (6.39) 0.28 (5.19) 0.35 (2.82) 0.32 (2.67) 0.45 (7.17) 0.33 (5.17) 0.51 (4.34) 0.48 (4.02) 0.26 (9.12) 0.06 (0.61) 0.32 (5.97) 0.29 (5.29) 0.09 (1.69) 0.01 (0.09) 0.19 (2.80) 0.18 (2.60) 0.15 (1.32) 0.26 (0.63) 0.08 (0.61) 0.09 (0.70) 0.14 (1.34) 0.42 (0.49) 0.06 (0.56) 0.07 (0.62) 1. IVτ τ 4 2. OLS (3.49) 0.24 (1.72) 0.11 (1.28) 0.12 (1.32) 0.26 (2.46) 0.03 (0.77) 0.85 (4.84) 0.83 (4.89) 0.27 (2.82) 0.14 (0.98) 0.81 (5.16) 0.80 (5.04) 0.49 (3.69) 0.17 (0.73) 0.48 (2.51) 0.46 (2.34) 0.04 (1.78) 0.02 (0.98) R 2 D.W IV IV IV IV IV IV IV IV
28 a b 7583 c d b d p Feldstein Kormendi No. y w w 1 τ g R 2 D.W III 83IV (3.45) (2.70) (0.77) (2.50) (0.68) I (2.26) (2.09) (0.56) (2.14) (0.86) IV (2.54) 0.37 (1.32) 0.23 (1.15) 0.12 (0.67) 0.07 (0.31) III 70I
29 4 II 1 Kormendi C t α 0 α 11 Y t α 12 Y t1 α 2 G t α 3 TR t α 4 TX t α 5 RE t α 6 GINT t 41 C Y G TR TX RE GINT Y t Y t1 G YD YTXRETRGINT 41α 2 0α 3 α 4 α 5α 6 0 α 4 0 α 2 α 3 α 6 α 4 α 3 α 6 0 α 5 α 5 0 S t b 0 b 11 Y t b 12 Y t1 b 2 G t b 3 TR t b 4 TX t b 5 RE t b 6 GINT t 42 S t YD t C t S t 43 α 4 b 4 1 b
30 Y Y 1 G TR TX RE GINT R 2 C S CB SB CY SY 0.67 (6.98) 0.15 (1.50) 0.92 (2.83) 0.16 (0.46) 0.02 (0.15) 0.35 (2.65) 0.91 (1.07) (0.31) 0.06 (0.65) 1.04 (3.37) 1.75 (5.40) 0.74 (3.68) 0.08 (0.62) 5.60 (6.89) (3.62) 0.17 (1.41) 0.53 (1.42) 0.30 (0.55) 0.29 (1.11) 0.05 (0.35) 2.22 (1.93) (0.89) 0.09 (0.73) 0.59 (1.65) 1.03 (1.97) 0.34 (1.38) 0.17 (1.18) 3.58 (3.24) (8.03) 0.07 (0.90) 1.04 (3.66) 0.34 (1.03) 0.29 (1.76) 0.39 (3.39) 0.09 (0.12) (0.68) 0.07 (0.83) 1.25 (4.26) 2.00 (5.94) 0.84 (4.87) 0.03 (0.22) 6.05 (7.58) D.W Y NNPG TR TX RE GINT C S 1 3. CS CBSB CYSY Y OLS 4. t TX α 4 OLS Y 5 TX b 4 41 α 4 b Miller1982α 4 b α α b 4 1 α 4 b
31 Y 0.70 (7.26) Y (0.76) G 1.29 (4.01) TR 0.86 (2.61) TX 0.96 (5.49) RE 0.55 (4.28) GINT 2.24 (2.96) 41 a 4 b 4 1 C S CB SB CY SY 0.01 (0.07) 0.25 (2.68) 0.73 (2.39) 1.17 (3.70) 0.04 (0.20) 0.24 (2.00) 2.98 (4.02) 0.60 (4.87) 0.07 (0.61) 0.56 (1.49) 0.02 (0.03) 0.58 (2.70) 0.14 (1.00) 0.17 (0.16) 0.23 (1.98) 0.30 (2.66) 0.57 (1.58) 0.75 (1.44) 0.42 (1.96) 0.25 (1.76) 1.48 (1.41) 0.71 (8.70) 0.08 (1.02) 1.19 (4.21) 0.74 (2.29) 1.03 (7.60) 0.49 (4.22) 2.26 (3.20) (0.001) 0.23 (2.95) 1.09 (3.70) 1.56 (4.70) 0.03 (0.23) 0.08 (0.64) 3.46 (4.80) Y Y 1 G TR TX RE GINT R 2 C S CB SB CY SY 0.52 (19.63) 0.09 (2.52) 0.40 (2.21) 0.45 (2.53) 0.04 (0.64) (0.032) 0.82 (2.40) (12.93) 0.23 (4.33) 0.79 (2.86) 0.24 (0.89) 1.13 (13.38) 1.00 (9.62) 0.98 (1.86) D.W II1983IV 2. CBSB OLS (4.18) 0.18 (1.69) 0.19 (0.90) 0.33 (1.30) 0.17 (1.74) 0.13 (1.56) 1.40 (2.66) (1.89) 0.35 (2.56) 0.20 (0.71) 0.42 (1.27) 0.63 (4.98) 0.62 (5.83) 0.39 (0.56) (23.07) 0.07 (1.96) 0.39 (2.10) 0.57 (3.01) 0.02 (0.28) 0.03 (0.41) 0.92 (2.55) (16.01) 0.17 (3.41) 0.83 (3.00) 0.02 (0.06) 1.03 (12.74) 0.92 (9.29) 0.66 (1.24)
32 TX α 4 0 Feldstein Kormendi TXX α C CB CY C CB CY 0.33 (2.90) 1.09 (14.93) 0.24 (1.42) 1.15 (8.91) 0.29 (2.07) 1.15 (13.81) 0.39 (5.01) 0.90 (27.07) 0.26 (3.03) 0.85 (15.61) 0.34 (3.81) 1.00 (22.16) R 2 D.W C CB CY C CB CY 0.06 (0.52) 0.33 (6.20) 0.02 (0.10) 0.30 (2.20) 0.07 (0.63) 0.33 (7.80) 0.21 (1.42) 0.29 (3.52) (0.002) 0.18 (0.96) 0.21 (1.51) 0.28 (4.16) R 2 D.W R 2 D.W α 4, TXRE TRGINT TXX TXRETRGINT
33 α 4 TXX 44 α 4 b α α α 3 α 3 0 TRREGINT TX TX 1 α Y Y G G () ()
34 Seater Mariano C t α 0 α 1 Y t α 2 Y t Yt α 3 G t α 4 G t G t α 5 TXX t 44 Y G Y G Y D logy t D logy t D tybeveridge Nelson Y Y t D logg t D logg t BeveridgeNelson G t 45 YY GG SeaterMariano 46 Y YY G GG TXX () () () (3.77) 8026 (0.63) (3.68) (4.73) (5.99) (3.03) (3.56) (0.37) (2.82) (1.70) (1.90) (0.87) (2.22) (1.01) (1.36) (1.29) (3.88) (0.98) R 2 D.W Y t G t EXBM t M t1 4 6 α α α Kormendi Aschauer 2 C t C t1 θg t1 θ G e t u t 47 e Gt 1 G t1 2 G t2 ωd t1 48
35 (0.46) (4.67) (29.80) (13.15) θ (1.54) (4.18) (2.07) (6.28) (6.75) (0.12) (1.57) (1.88) ω (0.23) (6.40) (1.54) 2 ω R C (0.36) ω R G0.994 Lr 2log Lu 1. R (1.10) (6.93) θ (5.79) (1.54) (8.65) (3.63) ω (0.64) R 2 C0.997 R 2 G (4.31) (6.80) (4.51) (4.40) (0.40) (1.76) (3.83) (0.64) ω (0.34) Lr 2log Lu 1 2 ω (0.41) (81.33) θ (1.18) 2896 (1.31) (6.85) (1.57) ω (2.63) 2 R C R 2 G (0.87) (4.81) (2.33) (1.23) (1.49) 3528 (1.64) (5.79) (0.26) ω (2.88) 47 Lr 2log Lu ω C t C t1 1 G t1 2 G t2 1 D t1 u t 49 G t 1 G t1 2 G t2 ω 1 D t1 410 DGTR GINTTX Gt 48 Gt G 47 G 48 C 4748 θ 1 θ θ 2 1 θω 1
36 OLS Asclauer 2 FP FP t1 1 2 YD t 3 FP t 4 FGt 5 WO t 6 i t 412 FP t t YD t t FG t t WO t t i t t FP 3 4 FG t 4 0 FPFG 2 ifp FG FG iifp i FP FG iii OLS OLS OLS OLS 4 FG 4 FP
37 i ii YD FP FG WO i R (4.77) 0.92 (9.90) 0.08 (1.01) 0.01 (1.01) 44.4 (0.62) (2.55) 0.97 (1.6.29) 0.09 (1.40) 0.02 (1.46) 66.8 (1.42) (2.80) 0.39 (2.34) 0.05 (0.20) 0.01 (0.62) 22.7 (0.61) (2.46) 0.85 (11.01) 0.14 (1.13) 0.01 (0.78) 15.1 (0.36) (4.90) 0.92 (9.82) 0.07 (0.84) 0.01 (0.93) 47.7 (0.65) (2.56) 0.97 (15.85) 0.08 (1.24) 0.02 (1.33) 72.8 (1.49) (2.87) 0.39 (2.33) 0.05 (0.20) 0.01 (0.36) 19.1 (0.49) (2.40) 0.84 (10.52) 0.17 (1.33) 0.02 (0.95) 20.4 (0.47) D.W III81 IV 2. YD FP iiii FG iiiwo i i GNP i 3. OLS OLS OLS OLS YD 2 WO 5 i F BlinderStiglitz1983 F 2 ΔX ΔX ΔR ΔD a( L) b( L) c ( L) X X R D ΔG d ( L) e 413 G X GNP GNP GNP R M 2 CDD G αlbl cldl Δ c i G b 0 i c 0 i F c i 0 GNP GN PGNP F
38 b0 HPMGGB HPMGB MONEYGGB MONEYGB HPMGGBG HPMGBG MONEYGGBG MONEYGBG c0 HPMGGB HPMGB MONEYGGB MONEYGB HPMGGBG HPMGBG MONEYGGBG MONEYGBG 411 F GNP GNP GNP HPM GGB bi0ci0 F 3. HPM MONEY M 2 CDGGB GB G b i 0 G GNP GNP causality
39
40 Atkinson-Stiglitz1980p.250 Dornbuch-Fischer1981p p p.56p b Feldstein OLS Feldstein 1θ1i i E1i i Hakkanson1970 T t Δ g Δ g Δ y0.030 Δ τ (2.43) (3.28) (2.29) ( Δ τ R D.W.2.08 t g y τ Δ Flavin1981Hayashi Y TX Kormendi 1970 SNA
41 3133 c y w dτ ssτ ss τ dτssτss g A D CPI c g 1965 I1983 I A D 1975 II1983 I 34 Notation c Personal consumption expenditurecvpc y National incomeypc w Wage and Salary incomeywpc τ taxpersoinal tax and nontax payments Personal contribution to special insurance Transfer payments from government to personstypsicp TRGPPC g Government expenditure, totalgvpc PC Price deflator for consumption 1960 III1983 IV 4149 C S Y G TR TX RE 4649 GINT EX B M M 2 CD TXX TXRETRGINT D GTRGINTTX I1983 IV 1CS Y TRTXREGINTEXB Y 50 2SNA SNA TXREEX RE RE 410 YD
42 FP (i) (ii) (i) FG (i) (ii) (i) WO i :1967 I1981 IV 1YDFPFGWO GNP i GNP 411 HPM MONEY M 2 CD GGB GB G :
43 Aschauer, D. A. (1985), "Fiscal Policy and Aggregate Demand" American Economic Review, Barro, R. J. (1974), "Are Government Bonds Net Wealth?" Journal of Political Economy, Vol. 86, No. 6, Barro, R. J. (1983), Macroeconomics, John Wiley & Sone. Bernheim, B. D. and K. Bagwell (1985), "Is Everything Neutral?" N. B. E. R. Discussion Paper. Beveridge, S. and C. R. Nelson (1981), "A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Composition with Particular Attention to Measurement of the 'Business Cycle.'" Journal of Monetary Economics, Blanchard (1985), "Debt, Deficits, and Finite Horizons" Journal of Political Economy, Blinder, A. S. and J. E. Stiglitz (1983), "Money, Credit Constraints and Economic activity,"american Economic Review, Feldstein, M. (1982), "Government Deficits and Aggregate Demand" Journal of Monetary Economics, 120. Flaven, M. A. (1981), "The Adjustment of Consumption to Changing Expectations about Future Income" Journal of Political Economy, Vol. 89, No. 5. Hakkanson, N. H. (1970), "Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions" Econometrica Vol. 38, No Hayashi, F. (1982), "The Permanent Income Hypothesis; Estimation and Testing by Instrument Variables" Journal of Political Economy, Vol. 90, No. 5. Kormendi, R. C. (1983), "Government Debt, Government Spending, and Private Secter Behavior" American Economic Review, Vol. 73, No. 5, Kotlikoff (1984), "Taxation and Savings: A Neoclassical Perspective" Journal of Economic Literature, Kurz (1984), "Capital Accumulation and the Characteristics of Private Intergenerational Transfers" Economica, 122. Miller, S. M. (1982), "Crowding Out: A Test of Some Direct Substitutability Hypothesis," Journal of Macroeconomics, Modigliani (1961), "Long-Run Implications of Alternative Fiscal Policies and the Burden of National Debt" Economic Journal, Mutoh (1985), "The Equivalence of the Burden of Internal and External Public Debt," Economics Letters, 17, Plosser, C. I. (1982), "Government Financing Decisions and Asset Returns," Journal of Monetary Economics, Seater (1982), "Are Future Taxes Discounted?" Journal of Money, Credit and Banking, Seater, J. J. and Mariano, R. S. (1985), "New Tests of the Life Cycle and Tax Discounting Hypothesis," Journal of Monetary Economics, Samuelson, P. A. (1980), Economics 11ed, Mc Graw-Hill, New York. (1981) 81 (1984a) (1984b) (1985) Vol.36, No (1982) Vol. 33, No (1981) 44 (1982) (1984)
global imbalances ) * 1
global imbalances 2 3 45 6 1) * 1 68 53 Denison 1958 2 Denison 1958 Feldstein and Fane 1973 1946 1968 Feldstein 19731978 David and Scadding 1974Furstenberg 1981Pitelis 1987 Poterba 1986 1948 1986 Bhatia
Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue Date Type Technical Report Text Version publisher URL
Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue 2012-06 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/23085 Right Hitotsubashi University Repository
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