203 0 5% 8% 204 4 204 205 0 0% 8% Peroi202 203 Iwaa20 205 0 0% 0%. 4 2. 2



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Transcription:

三 田 祭 論 文 消 費 税 増 税 時 の 政 策 オプション 3 本 の 矢 を 折 らないために 慶 應 義 塾 大 学 廣 瀬 康 生 研 究 会 荻 野 秀 明 川 邉 美 帆 財 津 薫 平 関 谷 裕 鏡 高 野 隼 一 橋 本 壮 広 橋 本 龍 一 郎 藤 村 和 輝 保 里 俊 介 203 年 月

203 0 5% 8% 204 4 204 205 0 0% 8% Peroi202 203 Iwaa20 205 0 0% 0%. 4 2. 2

3........................................ 3.2 DSGE......................... 5.3.............................. 5 2 DSGE 7 2......................................... 7 2.2......................... 5 3 24 3........................................ 24 3.2............................ 27 30 Appendix 3 47 2

. 32 GDP 237.9% 203 35 2. 90 30 20 2050 3500 200 7 3 3

202 3 2 OECD 2 0 5% 8% 203 0 8% 0% 2 DSGE 8% 0% DSGE 2 8% 0% 2 DSGE 2 2 4

.2 DSGE DSGE IS-LM GDP DSGE DSGE DSGE DSGE Forward-Looking DSGE.3 DSGE Iwaa20 Iwaa20 Smes and Wouers2003 3 Gali e al.2007 5

Iwaa20 Iwaa20 Blanchard and Peroi 2002 D.omer and H.omer 200 Peroi202 VA Peroi202 DSGE Peroi202 DSGE 3 3 6

2 DSGE 2. Iwaa20 Iwaa20 2. 7

Iwaa20 4 * 2.. n [0, ] i [0, ω] ω i C i I i B i K i z i E =0 β ε b C σ i hc σc ε l L i +σ l c + σ l β σ c σ l L i i h C ε b ε i.i.d. A ε b = ρ b ε b + η b, ε l = ρ l ε l + η. l + τ c C i + I i + Ψ z i K + B i P = τw l il i + τ k r k z ik i + τ d D i + B i P P 2. Ψz i z i τ c,τ,τ l k,τ d D i i P w i r k K i,b i * 8

[ ] ε i K i = δk i + S I i I i 2.2 I i δ S ε i A ε i = ρ i ε i + η i. z Ψz = 0 S = S = 0 Λ,Λ Q C i,b i,i i,k i,z i + τ c Λ = ε b C i hc σc + βε b h C+ hc β E [ Λ+ Λ P P + σc 2.3 ] = 2.4 ] ε i Q [ S i ε Q S i I i ε i I i I i I i I i [ Λ+ ε = βe Q + S i + I + i ε i ] + I + i Λ I i I i 2 I + i + 2.5 [ Λ+ Q = βe δq+ + τ Λ +r k +z k + i Ψ z + i ] + η q 2.6 τ k r k = Ψ z i 2.7 Q η q β = = δ + τ k r k Q = j [ ω, ] C N j L N j + τ c C N j = τw l jl N j 2.8 L i W i Calvo983 L N j W N j W i = W N j = W n 9

L i = L N i = L n L n L [ ] +λw, +λ L = L n w, dn 0 i.i.d. η w λ w, = λ w + η w [ max W L n 0 ] +λw, +λ L n w, dn W = w P 0 W nl ndn ξ w i γw W P i = W i P 2 γ w i W L ξw s s W max E W i subjec o s=0 i βξ w s C σ +s i hc+s σc ε l +s W +s i c + σ l W +s +λ w,+s λ w,+s + τ c +s C +s i + I +s i + ψ z +s i K +s i + B +si +s P +s = +λ τ+s l W+si W w,+s λ +s i w,+s L +s P +s W +s + τ+s k r k +s z +s ik +s i + τ+s k D +s i + B +s i P +s P +s +σ l L +s W i = W N j = W n W = [ ξ w W n λ w, W n = W i γw ] λw, P λ w, + ξw W n 2.9 P 2 0

2..2 f [0, ] Y f y f [ Y = y f 0 +λp, df η p i.i.d. λ p, λ p, = λ p +η p [ max P yf 0 p f y f +λp, +λp, y f df] ] 0 p fy fdf f y f = ε α k f α l f α Φ k k f = z k f l f Φ ε α A ε α = ρ a ε a + η a r k w mc = d f L = α α w α r k α ε a α α α α 2.0 d f = p fy f P mc y f + Φ r k w z K 2. D = P Y P mc Y + Φ 2.2

Calvo983 ξ p γp P p f = p f γ p P 2 f ξp s s P Y p max pf E βξ p s p+s f [p +s f P +s mc +s s=0 P = ξ p p f λ p, P +s + ξp P P 2 γ +λ p,+s λ p,+s Y +s P +s mc +s Φ] p p f λ p, λp, 2.3 2..3 G B τ c,τ l,τ k,τ d 3 Iwaa20 ˆτ c = ν c0 2.4 ˆτ l = ν l0 2.5 ˆτ k = ν k0 2.6 η g,η c, η d, η k i.i.d ν xi,x {c, l, k},i {, 2, 3 } ν x0 ν x = ν x + η x0 = ν x2 + η x. 2

ˆτ x = ν x0 = ν x + η x0 = ν 2 x2 + η x + η x0 = ν 3 x3 + η 2 x2 + η x + η x0. E ˆτ x + = E ν x0 + = E ν x = ν x + E η x0 + + E η x0 + = ν x2 + η x + E η+ x0 = ν 2 x3 + η x2 + η x + E η+ x0. = 3 = η x2 ηx3 = η x4 = = E ˆτ 2 x = E ν2 x0 = E ν x + E η2 x0 = ν x = ν0 x2 + η x = 0 E ˆτ 3 x = E ν3 x0 = E ν2 x + E η3 x0 = E ν x2 + E η2 x = ν0 x3 + η x2 = η x2 = E ˆτ 3 = E ˆτ 4 = = Iwaa20 Ĝ = η g 2.7 3

ˆ = ρ r ˆ + ρ r ϕ rπ ˆπ + ρ r ϕ ry Ŷ + η 2.8 π log P P 2 i.i.d. η 2..4 C L C = ωc i + ωc N j 2.9 L = ωl i + ωl N j L = L i = L N j B, I, K, D B = ωb i I = ωi i K = ωk i D = ωd i Y = ε a z K α L α Φ 2.20 Y = C + I + G + Ψz K 2.2 2..5 Iwaa20 Iwaa20 204 2 8% 4% 4% 8% 35% 4

2. α 0.3 β 0.99 δ 0.025 λ w 0.5 h 0.465 σ c.62 σ l 2.3 φ.904 ψ 0.46 ξ w 0.824 ξ p 0.432 γ w 0.2 γ p 0.595 ω 0.248 ρ r 0.934 ϕ ry GDP 0.254 ρ a 0.58 ρ b 0.43 ρ l 0.257 ρ i 0.8 ς 6.39 K GDP 2.2 Y C Y GDP 0.56 τ c 0.08 τ l + 0.08 τ k 0.0 τ d 0.35 2.2 2.2. 202 5

*2 Sims2002 Γ 0 s = Γ s + Ψ 0 ε + Π 0 η Γ 0,Γ,Ψ 0,Π 0 s ε η E η + = 0, s = Ψ s + Ψ ε ε Ψ,Ψ ε s VA 2.2.2 204 2 τ c = 0.08 8% 0% 0% 205 0 3 0 8 2 2 *2 6

2.2 2% 205 3.5%.5% Peroi202 Blanchard and Peroi 2002 4 7

2.3 2% PB 205 2 3 6 6 203 7.2 2.2.3.5% 2 6 203 5% 8

20 GDP GDP 8 SNA 203 35 20.8% 0%,GDP 6% Doi,Ihori and Kondo2002 Alesina and Peroi998 Alesina and Peroi998 960 994 OECD 20 GDP.5% 2 GDP.25% GDP.34%.22% Lamberini and Tavares2005 Lamberini and Tavares2005 Alesina and Peroi998 : =7:3 9

20 980 2005 5 6 20 GDP 0.25% -0.56% : 7:3 5 : =7:3 3 0.4 203 204 4 8% 7.2 8% 0% 3.2 3.2 2.2.4 3.2. 8% 0% 9% 2. 0.56% 3. 8.4% 4. 0.36% 3.5% 5. 3% 2-4 3.2 9% 3 3.2 9% 9% 5 3 20

5 2.4-0.5%,2,5,2-0.2% 5 - % 3,4 2.4 2.2 4 0.068 5 0.347 2.2. +% 0 0 0 0.04 2. +2% -0.56% 0 0 0.269 3. +2% 0-8.4% 0 0.69 4. +2% -0.36% -3.5% 0 0.068 5. +2% 0 0 3% 0.347 4 3 3.2 2

3.2 6.3% 6 4 6 4 0.0583 2.5 4 2.6 6 22

2.2.5 3 205 4 ω Iwaa20 3: 8.4% 6:6.3% 0% 4.5% 6 2% 2 23

3 3. 0.36% 3.5% 3.. 998 997 3% 5% 2 998 2 2 2 6000 3000 998 8 2 2 2 2 2 2002 978 998 % 6% % 2 24

2004 80 990 7.65% 25% 5 2% 99 992 GDP % 5% 0% 8 0 204 4 8% 205 0 0% 203 0 8% 204 4 0.36% 3.5% 3..2 0.36% 3.5% 3. 95 5% 4.55% 0 95 330 0% 9.% 97,500 330 695 20% 8.2% 427,500 695 900 23% 20.93% 636,000 900,800 33% 30.03%,536,000,800 40% 36.4% 2,796,000 25

3.2 25.5% 23.2% 3.26% 2.97% 4.82% 4.4% 48% 5.28% 4.8% 20.7% 0.36% 3.3 0% 9.% 4000 3640 2 3.4 PB. +% 0 0 0 0.04 3 2. +2% -0.56% 0 0 0.269 3.2 3. +2% 0-8.4% 0 0.69 3.2 4. +2% -0.36% -3.5% 0 0.068 3.2 5. +2% 0 0 3% 0.347 3.2 6. 2 +2% 0-6.3% 0 0.058 4 4 6,2,5 4 6 26

2.5 2.6 2 0.5% 2 6 4 75% Iwaa20 4 3.2 3.2. 3 2 2 ω Iwaa20 ω 0.248 % 27

3. 205 4 % 205 4 6 3.2.2 3 3% Iwaa20 GDP 7 28

3 29

DSGE 3 DSGE 3 3 0% 4 30

202 20 Λ,Λ Q L = E 0 β =0 ε b { } a σ c C i hc σc ε l +σ l L i +σ l + τ c C I + I I + Ψ z i K i + B i P { Λ τ w l il i τ k r k z ik i τ d D i [ ] P } ε l Λ Q {K i δk i + S I i C i,b i,i i,k i,z i I i I i L C i = εb C i hc σc Λ + τ c + βε b +h C+i hc Λ + τ c = ε b C i hct σc + βε b + h C+i hc L B i = Λ + E βλ + P Λ βλ+ = E P P + [ ] Λ+ P β E = Λ P + P + = 0 σc = 0 σc B i P } 3

[{ L I i = Λ Λ Q S βe [ Λ + Q + S ε i + I + i Q [ S ε i I i I i [ = βe Λ+ Λ Q + S ε i } ] ε i I i ε S i I i ε i I i I i I i I i ε i ] + I + i I i I i 2 I + i = 0 ] Q S ε i I i ε i I i I i I i + I +i ε i ] I + i + I i + I +i I i 2 L K i = Λ [ { Q + βe Λ+ Ψz+ i τ+ k r k + z + i } + Λ + Q + δ ] = 0 [ { Λ Q = βe Λ+ Ψz+ i τ+ k r k + z + i } + Λ + Q + δ ] [ Λ+ { Q = βe δq+ + τ Λ +r k +z k + i Ψ z + i } ] L z i = Λ τ k r k K i Λ Ψ z ik i = 0 Λ τ k r k K i = Λ Ψ z ik i τ k r k = Ψ z i 2.3-2.7 max E W i subjec o s=0 βξ w s C σ +s i hc+s σc ε l +s W +s i c + σ l W +s +λ w,+s λ w,+s + τ c +s C +s i + I +s i + ψ z +s i K +s i + B +si +s P +s = +λ τ+s l W+si W w,+s λ +s i w,+s L +s P +s W +s + τ+s k r k +s z +s ik +s i + τ+s k D +s i + B +s i P +s P +s +σ l L +s E s=0 βξ w s P +σ c +s εl +s + s igma l σc σ c C +s i hc+s + τ c +s C +s i + I +s i + Ψz +s ik +s i + B+si τ+s k r k +s z +s ik +s i τ+s d D+s i P +s τ+s l σc W +s i σ c +s P +s + B +s i P +s +σc 32

E +si = E s=0 P+s P +s 2 γw W +s i = = s k= π +k γ w W i βξ w s P +σc +s εl +s + s igma l + τ c +s C +s i + I +s i + Ψz +s ik +s i + B+si +s P +s + B +s i P +s τ+s k r k +s z +s ik +s i τ+s d D+s i P +s τ+s l σc s k= π+k γ w σ c σ c W i 2 σ c +σc 3. [ max P yf 0 y f [ + λ p P y f 0 +λp, +λp, y f df] P y +λp, df λ p +λ p ] λ p λ p 0 + λ p y f p fy fdf +λ p +λ y f p p f = 0 p f = 0 p f y f = P +λ p λ p Y Y +λ p Y = = = 0 p f P p f 0 P λ p P Y +λ p +λ p λ p λ p Y 0 Y +λ p +λ p df df +λ p +λ p p f λ p df P = 0 λ p p f λ p df 33

min r k k f + w l f l, k f subjec o y = ε a k f α l f α L = r k k f + w l f + mc y ε a k f α l f α Φ l, k f 3.2 3.3 L = w f αmc ε a l k f α l f α 3.2 L k f = rk αmc ε a k f α l f α 3.3 r k w = l f = α α αl f α k f r k w k f L = α α r k w z K 3.4 2. 3.3 3.2 r k αmc ε a k α f α r k α k f = 0 α w α r k = αmc ε a r k α α w r k α w α ε a α α α α = mc 3.5 2.0 max E βξ p s p+s f p +s f P +s mc +s pf s=0 P +s +λ p,+s λ p,+s Y +s P +s mc +s Φ 34

p f = P P 2 p f E βξ p s p f +λ s k= P +s π p,+s λ λ +k p,+s p f s p,+s mc+s π γ p +k Y +s P +s P +s s=0 E s=0 E s=0 E s=0 βξ p s P +s Y +s βξ p s Y +s βξ p s Y +s p f s λ p,+s k= πγ p +k P +s mc +s + λ p,+s p f s λ p,+s P +s p f P +s λ p,+s λ p,+s k= k= πγ p +k P +s p f s k= πγ p λ p,+s +k P +s mc +s + λ p,+s p f s λ p,+s s k= π γ p +k +λ p,+s λ p,+s [ p f P +s k= πγ p +k P +s s k= π γ p +k P +s +λ p,+s λ p,+s +λ p,+s λ p,+s = 0 = 0 mc +s + λ p,+s ] = 0 P +s = P P P + P + P +2 P+s P +s = P π + π +2 π +s = P s k= E s=0 βξ p s Y +s p f P p o = p f P E s=0 βξ p s Y +s p o s k= π +k π γ p +k [ p f P +s +λ p,+s λ p,+s s k= s k= [ π +k p o k= π +k γ p s π +k π γ p +k +λ p.+s λ p,+s π +k mc +s + λ p,+s ] = 0 ] π +k γ p mc +s + λ p,+s = 0 3.6 ˆx = log x x 35

2.3 + τ c Λ = ε b C i hc σc + βε b h C+ hc + τ c ΛˆΛ + Λτ cˆτ c = σ c C hc σ c CĈ σ c C hc σ c hcĉ + C hc σ c C hc σ c C E Ĉ+ σ c ˆε b + β σ c C hc σ c hcĉ + C hc σ c ˆε b = σ c C σ c h σ c Ĉ hĉ + βe Ĉ + βhĉ σc +C σ c h σ c + βˆε b = C σ c h σ c σ c βhĉ + σ c hĉ βσ c E Ĉ+ + h + βˆε b 2.3 C σ c h σ c + + τ c ΛˆΛ + C σ c h σ c + Λτ cˆτ c = σ c βhĉ + σ c hĉ βσ c E Ĉ + + h + βˆε b 3.7 + τ c Λ = ε b C i hc σc = + τ c Λ = C hc σ c C hc σ c Λ = + τ c σc = C h σ c + τ c C σ c h σ c + Λ = h + τ c 3.8 3.7 3.8 h 2 + τ c ˆΛ + h + τ c τ cˆτ c = σ c βhĉ + σ c hĉ βσ c E Ĉ + + h + βˆε b 3.9 36

2.4 β E [ Λ+ Λ P P + ] = = log β + log + log E Λ + log Λ + log P log E P + = log = 0 log β + log + log Λ log Λ + log P log P = 0 ˆ + E ˆΛ+ ˆΛ + ˆP y E ˆP+ = 0 ˆΛ E ˆΛ+ = ˆ + ˆP y E ˆP+ 3.0 2.5 ] ε i Q [ S i ε Q S i I i ε i I i I i I i I i [ Λ+ ε = βe Q + S i + I + i ε i ] + I + i Λ I i I i 2 I + i + = Q ˆQ SQ ˆQ QS Î + QS Î QS ˆε i { } S QQ + [S + S ] QÎ [S + S ] QÎ + [S + S ] Qˆε i { βs = Q ˆQ } + [S + 2S ] QβÎ+ [S + 2S ] QβÎ +βqs ˆΛ + βqs ˆΛ + [S + S ] βqˆε i + S = S = 0 [ ] [ ] Q ˆQ QS Î Î + ε i = S Qβ Î + + Î + ˆε i + S + βî = ˆQ + S Î + βs Î+ + S ˆε i + ε i S x x= S x x= = { [x ] 2 /2S} { } 2x = 2S = 2 2S x= x= x= = S 37

Î = + β Î + β + β E Î+ + ς + β ˆQ βe ˆε i + ˆε i + β 3. 2.6 Q =, β = = δ + τ k r k [ Λ+ Q = βe δq+ + τ Λ +r k +z k + i Ψ z + i ] + η q [ = ˆQ = β δ + τ k r k Λ ΛE ˆΛ + Λ Λ 2 ΛˆΛ + Λ ] δe ˆQ+ + τ k r k E ˆr + k τ k r k E ˆτ + + ˆη q Λ [ δ + τ k r k E ˆΛ+ ˆΛ = β = + δe ˆQ+ + τ k r k E ˆr k + τ k r k E ˆτ + ] + ˆη q E ˆΛ+ ˆΛ + δ δ + τ k r k E ˆQ + + τ k r k δ + τ k r k E ˆr k + 3.0 E ˆΛ+ ˆΛ = E ˆP+ ˆP ˆ E ˆP+ ˆP = E ˆπ + δ ˆQ = ˆ E ˆπ + + δ + τ k r k E ˆQ + τ k r k + δ + τ k r k E ˆr + k 2.2 S = 0 [ K i = δk i + S = K ˆK = δk ˆK + IÎ S I I τ k r k δ + τ k r k E ˆτ k + + ˆη q ] ε i I i I i I i I I I ˆε i S Î + S I 2 Î I I 3.2 2.2 = δk ˆK + IÎ S I ˆε i S Î + S I 2 Î = δk ˆK + IÎ ˆK = δ ˆK + I Î K K = δk + I I K = δ 38

ˆK = δ ˆK + δî 3.3 2.7 τ k r k = Ψ z = τ k r k = Ψ z i = τ k r kˆr k τ k r kˆτ k = Ψ zẑ ˆr k = τ k r k Ψ Ψ ẑ τ k τ k ˆτ k = Ψ Ψ ẑ ψ = Ψ Ψ ψ ẑ = ψ [ˆr k τ k ] τ k ˆτ k 3.4 3.6 ˆλ p,+s = log+λ p,+s +λ p E s=0 βξ p s p F Y +s P s k= π +k [ p f P π +k γ p s k= π +k +λ p.+s λ p,+s ] π +k γ p mc +s + λ p,+s = 0 E s= = E βξ p [ˆp s o + s=0 E s=0 E βξ p s [ˆp o ] s γ pˆπ +k ˆπ +k ˆmc +s ˆλ p,+s = 0 k= ] s ˆπ +k γ pˆπ +k ˆmc +s ˆλ p,+s = 0 k= s=0βξ p s [ s k= βξ p s ˆπ +k γ pˆπ +k + βξ p ˆπ +k γ pˆπ +k + ˆmc +s + ˆλ p,+s ] = βξ p s ˆmc +s + ˆλ p,+s = ˆp o s=0 + βξ p E s=2 βξ p s ˆπ +k γ pˆπ +k + βξ p 39 βξ p ˆp o βξ p s ˆmc +s + ˆλ p,+s = βξ p ˆp o s=

ˆp o βξ p E ˆp o + = βξ p E ˆπ + γ pˆπ + βξ p ˆmc + ˆλ p. 3.5 2.3 P = ξ p p f λ p, P λ p = ξ p p f λ p, = ξ p = ξ p [ p f P p o λp + ξp P P 2 + ξp P P 2 γ γ λp + ξp π γ p + j= = 0 = ξ p λp ˆp o λ p { ˆp o = ˆp o j + ξp j j= k= j= ξ j p ˆp o = ξp j ˆp o j + j ˆp o = j= p o jξ j p ξp j j= p p p f p f λ p, ] λ p f p, P { j π k γ p { k= ˆp o j + λ p, λ p, π k+ } λp j } γ pˆπ k ˆπ k+ k= } j ˆπ k+ γ pˆπ k k= ξp j j= k= γ pˆπ k ˆπ k+ = ξ p j= ξ p ξ p ˆp o = j=2 ξ j p ˆp o j + ξ p ξ j p ˆp o j + ξ p j γ pˆπ k ˆπ k+ ξp j γ pˆπ j ˆπ j+ j= ξp j γ pˆπ j ˆπ j+ j= ξp j γ pˆπ j ˆπ j+ j=2 ˆp o ξ p ˆp o = γ pˆπ ˆp o = ξ p ξ p γ pˆπ ˆπ ξ p ξ p ˆπ γ pˆπ 40

3.5 ξ p ξ p ξ p ˆπ γ pˆπ βξ p ξ p E ˆπ + γ pˆπ ξ p ξ p ˆπ γ pˆπ = = βξ p E ˆπ + γ pˆπ + βξ p βξp ξ p ˆmc + ˆλ p, ξ p E ˆπ + γ pˆπ + βξ p ˆπ γ pˆπ = β E ˆπ + γ pˆπ + βξ p ξ p ˆmc + ξ ˆλ p, p + βγ p ˆπ = γ pˆπ + βe ˆπ + + βξ p ξ p ˆmc + ξ ˆλ p, p ˆπ = γ p β ˆπ + E ˆπ + + βξ p ξ p + βγ p + βγ p ξ p + βγ p 3.8 ˆmc = mc ŵ + αˆr k ˆε a λ p, = λ p + η p ˆmc + ˆλ p, ˆmc + ˆλ p, ˆπ = + β + βγ p E ˆπ + + γ p + βγ p ˆπ βξ p ξ p + βγ p ξ p [ αˆr k + α ŵ ˆε a + η p ] 3.6 2.8 + τ c C N j = τw l jl N j = C N τ cˆτ c + + τ c C N Ĉ N C N Ĉ N + τ c + τ cˆτ c Y = wl N τ lˆτ l + τ l L N wŵ + τ l N wl ˆLN = wl N τ l ŵ + ˆL τ lˆτ l C N Y [ĈN + τ c + τ cˆτ c 2.0 ] = w L Y [ τ l ŵ + ˆL τ lˆτ ] l 3.7 mc = w α r k α ε a α α α α = log mc = α log w + α log r k log ε a α log α α log α log mc = α log w + α log r k α log α α log α 4

ˆmc = mc ŵ + αˆr k ˆε a 3.8 2. L = α α r k w z K log L = log α + log r k + log z + log K log α log w log L = log α + log r k + log z + log K log α log w ˆL = ŵ + ˆr k + ẑ + ˆK 3.9 2.2 D = P Y P mc Y + Φ = D ˆD = P Y Ŷ + Y P ˆP Y + Φ mcp ˆP Y + Φ P mc ˆmc P mcy Ŷ D ˆD P Y P mc Y + Φ ˆP = P Y Ŷ Y + Φ P mc ˆmc P mcy Ŷ 2.2 D = P Y P mc Y + Φ D ˆD ˆP = P Y mc Ŷ P Y + Φ mc ˆmc P Y + Φ = φ ˆd Y D P Y ˆd = mc Ŷ mcφ ˆmc 3.20 2.9 3. ŵ = β + β E ŵ + + + β ŵ + β + β E ˆπ + + βγ w + β ˆπ + γ p + β ˆπ + β [ ŵ σ l ˆL βξ w ξ w + +λ wσ l λ w ξ w σ c Ĉ h hĉ ˆε l η w τ l τ l ˆτ l τ c + τ c ˆτ c ] 3.2 42

2.9 C = ωc i + ωc N j = CĈ = ωc Ĉ + ωc N Ĉ N Y C Y = ωc Ĉ Y + ω CN Ĉ N Y 2.20 Y = ε a z K α L α Φ = Y Ŷ = K α L αˆε a + αk α L α ẑ + αk α L α K ˆK + αk α L α LˆL 2.20 Y = K α L α Φ Y + Φ = K α L α Y Ŷ = Y + Φ ˆε a + α Y + Φ ẑ + α Y + Φ ˆK + α Y + Φ ˆL Y Φ Y = φ Ŷ = φ ˆε a + αẑ + α ˆK + αˆl 3.22 2.2 z = Y = C + I + G + Ψz K = Y Ŷ = CĈ + IÎ + GĜ + Ψ Kẑ + ΨK ˆK 2.7 τ k r k = Ψ Ψ = 0 Y Ŷ = C Ĉ + δ K Y Y Î + G Y Ĝ + τ k r k K Y ẑ 3.23 43

DSGE hˆλ + h + τ c ˆτ c = σ c βhĉ + σ c hĉ βσ c E Ĉ + + h + βˆε b ˆΛ = E ˆΛ+ + ˆ + ˆP y E ˆP+ 3.24 q Î = + β Î + β + β E Î+ + ς + β ˆQ βe ˆε i + ˆε i + β δ ˆQ = ˆ E ˆπ + + δ + τ k r k E ˆQ + τ k r k + δ + τ k r k E ˆr + k τ k r k δ + τ k r k E ˆτ k + + ˆη q 3.25 3.26 ẑ = ψ [ˆr k τ k + r k ] τ k ˆτ k 3.27 ˆK = δ ˆK + δî 3.28 ŵ = β + β E ŵ + + + β ŵ + β + β E ˆπ + + βγ w + β ˆπ + γ p + β ˆπ + β [ ŵ σ l ˆL βξ w ξ w + +λ wσ l λ w ξ w σ c Ĉ h hĉ ˆε l η w τ l τ l ˆτ l τ c + τ c ˆτ c ] 3.29 C N Y [ĈN + τ c + τ cˆτ c ] = w L Y [ τ l ŵ + ˆL τ lˆτ ] l 3.30 ˆmc = mc ŵ + αˆr k ˆε a 3.3 ˆL = ŵ + ˆr k + ẑ + ˆK 3.32 44

D P Y ˆd = mc Ŷ mcφ ˆmc 3.33 ˆπ = + β + βγ p E ˆπ + + γ p + βγ p ˆπ βξ p ξ p + βγ p ξ p [ αˆr k + α ŵ ˆε a + η p ] 3.34 ˆτ c = ν c0 3.35 ˆτ l = ν l0 3.36 ˆτ k = ν k0 3.37 x {c, l, k},i {, 2, 3 } ν x0 ν x = ν x + η x0 3.38 = ν x2 + η x 3.39. 3.40 ˆ = ρ r ˆ + ρ r ϕ rπ ˆπ + ρ r ϕ ry Ŷ + η 3.4 C Y = ωc Ĉ Y + ω CN Ĉ N 3.42 Y Ŷ = C Ĉ + δ K Î + G Y Y Y Ĝ + τ k r k Ŷ = φ ˆε a + αẑ + α ˆK + αˆl K Y ẑ 3.43 3.44 ˆε b = ρ bˆε b + η b 3.45 ˆε i = ρ iˆε i + η i 3.46 45

ˆε l = ρ lˆε l + η l 3.47 ˆε a = ρ aˆε a + η a 3.48 46

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