DGE DGE (1) ( 1

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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 Tokyo,Japan

2 DGE DGE (1) ( 1

3 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) Ono 2001) (2) ( ) (3) 3 (2) (3) Tsuzuki and Inoue(2010) Inoue and Tsuzuki (2011) 2 Benhabib et al. (2001) 2

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

5 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

6 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

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

8 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

9 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

10 = 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

11 = 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

12 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 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

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

13 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

14 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

15 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

16 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

17 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

18 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

19 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

20 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

21 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

22 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

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

24 [1] (1995) [2] (2011) 21 COE-GLOPE Working Paper Series, 48 [3] (1992) [4] (2004) 23-3 [5] (2000) [6] (2003) [7] (2012) 12-J-3 [8] Benhabib, J., S. Schmitt-Grohe and M. Uribe (2001) The Perils of Taylor Rules, Journal of Economic Theory, 96, pp [9] Blanchard, Olivier J. and Kiyotaki, Nobuhiro (1987) Monopolistic Competition and the Effects of Aggregate Demand, American Economic Review, 77, pp [10] Dixit, Avinash K. and Stiglitz, Joseph E. (1977) Monopolistic Competition and Optimum Product Diversity, American Economic Review, 67, 3, pp [11] Eggertsson, Gauti and Woodford, Michael (2003) The Zero Bound on Interest Rates and Optimal Monetary Policy, Brookings Papers on Economic Activity, 1, pp [12] Inoue, Tomohiro and Tsuzuki, Eiji (2010) A New Keynesian Model with Technological Change, Economics Letters, 110, 3, pp

25 [13] Krugman, Paul (1998) It s Baaack: Japan s Slump and the Return of the Liquidity Trap, Brookings Papers on Economic Activity, 2, pp ( 2003 ) [14] Murota, Ryu-ichiro and Yoshiyasu Ono (2011) Growth, Stagnation and Status Preference, Metroeconomica, 62(1), pp [15] Ono, Yoshiyasu (2001) A Reinterpretation of Chapter 17 of Keynes s General Theory: Effective Demand Shortage Under Dynamic Optimization, International Economic Review, 42, pp [16] Rotemberg, Julio J. (1982) Sticky Prices in the United States, Journal of Political Economy, 90, 6, pp [17] Tsuzuki, Eiji and Inoue, Tomohiro (2010) Policy Trade-off in the Long Run: A New Keynesian Model with Technological Change and Money Growth, Economic Modelling, 27, 5, pp

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