DGE DGE 2 2 1 1990 1 1 3 (1) ( 1

早 稲 田 大 学 現 代 政 治 経 済 研 究 所 ゼロ 金 利 下 で 量 的 緩 和 政 策 は 有 効 か? -ニューケインジアンDGEモデルによる 信 用 創 造 の 罠 の 分 析 - 井 上 智 洋 品 川 俊 介 都 築 栄 司 上 浦 基 No.J1403 Working Paper Series Institute for Research in Contemporary Political and Economic Affairs Waseda University 169-8050 Tokyo,Japan

DGE DGE 2 2 1 1990 1 1 3 (1) ( 1

T O 1: Benhabib et al. (2001) DGE(Dynamic general equilibirum) 2 R = R(π) π R 1 R = r + π r Benhabib et al. (2001) R = R(π) 2 T L Benhabib et al. (2001) 2 1992 Ono 2001) (2) ( 2000 2003 8 ) (3) 3 (2) (3) Tsuzuki and Inoue(2010) Inoue and Tsuzuki (2011) 2 Benhabib et al. (2001) 2

T L O 2: L DGE Rotemberg (1982) 2 2 (2011) 2 γ π2 2 γ π π 3 γ (π π ) 2

2 3 2 4 Res D (1) K (2) B (3) Res 3 D = K + B + Res D Res σ D M ( Res/ σ) K M ( D M Res B) K M 3 ( 1995) ( 1995) 4 4

R 0 R 0 (1) (K M ) (2) (R 0 ) K M1 K M2 R 0 O P Z Z 3: 3 R K 5 K M1 P K M2 R 0 Z Z 5 3 Krugman(1998) 1 2 K M Krugman(1998) M M K M 5

R 0 Z P Z 2 1 6 1: 6 Murota and Ono(2011) Murota and Ono(2011) 2 Murota and Ono(2011) DGE Murota and Ono(2011) 6

7 T L R 0 O 4: 4 R π R 0 7 (2004) Krugman(1998) Eggertsson and Woodford(2003) Benhabib et al. (2001) 7

R 0 R 0 T L 2 T R 0 R 0 L 8 3 i (i [0, 1]) i j (j [0, 1]) j 8 8

= y y = k α h 1 α (3.1) α 0 < α < 1 k h Π f Π f = py W h Rpk (3.2) p W R Π f w = (1 α)ĥ α (3.3) r = αĥ1 α (3.4) w( W/p) r( R π) ĥ ĥ h/k 9

= 9 h [ 1 h = 0 φ 1 φ hi ] φ φ 1 di h i i φ(> 1) h i = ( ) φ Wi h (3.5) W W i j W [ 1 W = 0 ] 1 W 1 φ 1 φ i di (3.6) h i h i = zl i l i z z g(= ż/z) z h i D B h A A = D + B h (3.7) R b 9 Dixit and Stiglitz (1977) Blanchard and Kiyotaki (1987) 10

A = R b B h + W i h i cp + X g + X b (3.8) c X g X b (3.8) ȧ = ra + w i h i c R b d + x g + x b (3.9) a( A/p) d( D/p) w i ( W i /p) h i x g X g /p x b X b /p i c d l i 10 ln c + δ ln d l1+ψ i 1 + ψ γ 2 ω2 i (3.10) δ ln d δ(> 0) ψ(> 0) ω i W i Ẇ i /W i γ 2 ω2 i 11 γ γ 0 γ > 0 i [ ] max ln c + δ ln d l1+ψ i c,d,ω i 0 1 + ψ γ 2 ω2 i e ρt dt subject to ȧ = ra + w i h i c R b d + x g + x b Ẇ i = ω i W i ( ) φ Wi h i = h W h i = zl i 10 c c i d d i c d A B h 11 Rotemberg (1982) 11

ρ(> 0) l i = l, ω i = ω, h i = h ( i [0, 1]) ċ c + π + ρ = R = δ c d ] ω = ω [ρ φ l1+ψ hw + (φ 1) γω γcω (3.11) (3.12) l ω (3.11) (3.12) B Res B c Res(0) = B c (0) Res= B c (1) (2) 2 (1) π R R = R(π) = R + τ(π π) (3.13) R π τ(> 1) 12

R π R π R = r + π r (3.4) r = α(ĥ ) 1 α (2) θ Res Y ( py) X b = ζy ζ(> 0) X b (= ζy ) = Ḃall B all B all B B c (B all = B +B c ) B c Res B all = B +Res j k j = k [ 1 k 0 η 1 η kj ] η η 1 dj η(> 1) ( ) η Rj k j = k (3.14) R 13

R j j R [ 1 R = 0 ] 1 R 1 η 1 η j dj (3.15) R K j D j D M σ D M Res/ σ j D j Res B K j D j = Res + B + K j 12 j Π j Π j = R b B + (R j υ)k j (3.16) 12 Res Res j B B j Res B 14

υ(> 0) υ R j R j K j j 13 max Π j = (R j υ)k j + R b B (3.17) R j ( ) η Rj subject to K j = K (3.18) R D j = Res + B + K j (3.19) ( D j D M Res ) (3.20) σ K( kp) R j η η 1 υ with equality when D j < D M (3.21) (D j = D, j [0, 1]) (R j = R, j [0, 1]) R b R (R b = R) η 14 R 0 υ η 1 R 0 (3.21) R R 0 with equality when D < D M (3.22) 13 B all (= B + Res) Res Res B 14 R b = R υ 2 15

4 D = D M R > R 0 D < D M R = R 0 2 ERD ERD Res σd ERD = Res σd = (σ σ)d σ D = D M σ = σ σ σ ERD ERD = (σ σ)d = 0 (4.1) σ(= σ) Res θ D(= Res/ σ) θ d θ θ d = θ σ σ σ σ ERD ERD = (σ σ)d 0 (4.2) 16

R(= R 0 ) (3.11) Ṙ R = ċ c d d = 0 (4.3) θ d ( Ḋ/D) θ d Ḋ D = d d + π = ċ c + π = R 0 ρ (4.4) θ d R 0 ρ ρ θ θ d ρ 17

5 y = c + I ĉ ĉ ĥ = αĥ1 α ρ ĥ1 α + ĉ (5.1) ĥ = 1 α (R αĥ1 α ω) (5.2) l ĥ = l ĥ + ĥ1 α ĉ g = 1 α (R αĥ1 α ω) + ĥ1 α ĉ g (5.3) [ ] ω = ω ρ φ l1+ψ γω + (φ 1)(1 α)ĥ1 α γωĉ (5.4) ĉ c/k R = R + τ(π π) π = α ĥ/ĥ + ω ĉ = ρ + g α g (5.5) ( ) 1 ρ + g ĥ 1 α = (5.6) α [ γπ l ρ = φ + φ 1 ] 1 (1 α)(ρ + g) 1+ψ (5.7) φ ρ + g gα ω = π = π (5.8) r = α(ĥ ) 1 α = g + ρ R = g + ρ + π R = R(π) = g + ρ + π + τ(π π) (5.9) 18

Ṙ R ĉ ĉ ĥ = R (θ + ρ) (5.10) = αĥ1 α ρ ĥ1 α + ĉ (5.11) ĥ = 1 α (R αĥ1 α ω) (5.12) l ĥ = l ĥ + ĥ1 α ĉ g = 1 α (R αĥ1 α ω) + ĥ1 α ĉ g (5.13) [ ] ω = ω ρ φ l1+ψ γω + (φ 1)(1 α)ĥ1 α γωĉ (5.14) R = θ + ρ (5.15) ĉ = ρ + g α g (5.16) ( ) 1 ρ + g ĥ 1 α = (5.17) α [ γπ l ρ = φ + φ 1 ] 1 (1 α)(ρ + g) 1+ψ (5.18) φ ρ + g gα ω = π = θ g (5.19) (5.19) π θ g l π 19

l n (γ 0) l n = [ φ 1 φ ] 1 (1 α)(ρ + g) 1+ψ ρ + g gα (5.20) l l n π = 0 ( π = 0) θ g (θ = g) 6 ĉ ĉ ĥ = αĥ1 α ρ ĥ1 α + ĉ (6.1) ĥ = 1 α (R 0 αĥ1 α ω) (6.2) l ĥ = l ĥ + ĥ1 α ĉ g = 1 α (R 0 αĥ1 α ω) + ĥ1 α ĉ g (6.3) [ ] ω = ω ρ φ l1+ψ γω + (φ 1)(1 α)ĥ1 α γωĉ (6.4) 20

ĉ = ρ + g α g (6.5) ( ) 1 ρ + g ĥ 1 α = (6.6) α [ γπ l ρ = φ + φ 1 ] 1 (1 α)(ρ + g) 1+ψ (6.7) φ ρ + g gα ω = π = θ d g = R 0 ρ g (6.8) R 0 ρ g ρ g π (= ω ) (6.7) (5.20) r r = g + ρ R = g + ρ + π r (γ 0) 21

Krugman(1998) Eggertsson and Woodford(2003) g r (= g + ρ) g 1% 15 R(= π + r) 7 DGE 2 2 15 (2012) 3 22

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