価格弾力性の異質性を考慮したフィリップス曲線の推計

日 本 銀 行 ワーキングペーパーシリーズ 価 格 弾 力 性 の 異 質 性 を 考 慮 した フィリップス 曲 線 の 推 計 代 田 豊 一 郎 * toyoichirou.shirota@boj.or.jp No.06-J-16 2006 年 7 月 日 本 銀 行 103-8660 日 本 橋 郵 便 局 私 書 箱 30 号 * 日 本 銀 行 調 査 統 計 局 経 済 分 析 担 当 日 本 銀 行 ワーキングペーパーシリーズは 日 本 銀 行 員 および 外 部 研 究 者 の 研 究 成 果 をと りまとめたもので 内 外 の 研 究 機 関 研 究 者 等 の 有 識 者 から 幅 広 くコメントを 頂 戴 する ことを 意 図 しています ただし 論 文 の 中 で 示 された 内 容 や 意 見 は 日 本 銀 行 の 公 式 見 解 を 示 すものではありません なお ワーキングペーパーシリーズに 対 するご 意 見 ご 質 問 や 掲 載 ファイルに 関 する お 問 い 合 わせは 執 筆 者 までお 寄 せ 下 さい 商 用 目 的 で 転 載 複 製 を 行 う 場 合 は 予 め 日 本 銀 行 情 報 サービス 局 までご 相 談 ください 転 載 複 製 を 行 う 場 合 は 出 所 を 明 記 してください

2006 7 NKPC NKPC JEL Classification: E31,E32 (toyoichirou.shirota@boj.or.jp) 1

1 (New Keynesian Phillips Curve, NKPC) NKPC NKPC NKPC 1 2 (2002) 90 1 (1) (2) 2 2

Kalecki (1938)Rotemberg and Saloner (1986) Bils (1985) Gali (1994) sluggishness NKPC 2 NKPC 3 4 5 6 2 Gali (1994) 2 Gali (1994) 3 2 Kiley (1997) 1 Taylor staggered Kiley (1997) Taylor (amplification mechanism) Chari, Kehoe, and McGrattan (2000) (1)Rotemberg-Calvo (2) 3

3 2.1 C t z(z [0, 1]) C t (z) Dixit and Stiglitz CES C t ( ) ɛ Pt (z) C t (1) C t (z) = P c t C t = [ 1 C 0 t(z) ɛ 1 ɛ dz] ɛ ɛ 1 Pt c = [ 1 P 0 t(z) 1 ɛ dz] 1 1 ɛ ɛ > 1 2.2 Gali (1994) I t z I t (z) Dixit and Stiglitz CES 4 I t ( ) η Pt (z) I t (z) = I t (2) P I t I t = [ 1 I 0 t(z) η 1 η η dz] η 1 Pt I = [ 1 P 0 t(z) 1 η dz] 1 1 η η > 1 3 1 4 CES 4

2.3 z (1), (2) N t (z) K t (z) 0 < α < 1 Calvo (1983) (1 ς),0 < ς < 1 5 z E t j=0 { [ ] } ς j Pt (z) Λ t,t+j MC Pt+j c t+j Y t+j (z) Λ t,t+j β j [u (C t+j )/u (C t )] MC Y (z) z C(z) + I(z) Calvo (1983) P c = P I P 6 Calvo NKPC P t (z) = E t j=0 ςj Λ t,t+j MC t+j [ɛc t+j (z) + ηi t+j (z)] E t j=0 ςj 1 Λ t,t+j [(ɛ 1)C Pt+j c t+j (z) + (η 1)I t+j (z)] (3) 2.4 (3) ( ) ˆπ t = φ 0 ˆmc t + φ 1 E tˆπ t+1 + φ 2 it /y t (4) 5 Calvo Rotemberg Roberts (1995) Calvo Rotemberg 6 5

ˆx ( x) ˆp c t = ˆp I t ˆp t ˆπ t = ˆp t ˆp t 1 7 (1 ς)(1 βς) φ 0 = ςx φ 1 = β (ɛ η)φ 0 ĪȲ φ 2 = (ɛ c + η ĪȲ )(ɛ c + η 1) Ȳ Ȳ ĪȲ X = 1 + ɛ c 1 ɛ + ɛmc Ȳ ɛ c + η ĪȲ 1 + η Ī 1 η + ηmc Ȳ ɛ c + η ĪȲ 1 Ȳ Ȳ MC = ɛ c Ȳ + η ĪȲ 1 ɛ c Ȳ + η ĪȲ (η, ɛ, ς, β) 2.5 ɛ η ξ t = C t Y t ɛ + I t Y t η ξ ξ 1 2.6 (4) 1 2 NKPC 3 7 2 6

φ 2 (ɛ η) (ɛ < η) φ 2 (ξ t ) (ɛ > η) φ 2 (4) 8 2.7 NKPC NKPC NKPC η = ɛ φ 2 = 0 (4) NKPC NKPC 3 NKPC 2 Gali and Gertler (1999) Sbordone (2002) 2 Calvo NKPC 8 Gali (1994) η > ɛ 7

E t π t+1 9 Gali and Gertler (1999) GMM Sbordone (2002) Campbell and Shiller (1987) VAR GMM 10 11 NKPC (4) 3.1 (ULC) 1213 (4) 9 10 (2005) ULC 11 ULC Sbordone (2002) 12 (4) ˆmc t ˆmc t = rulc t MC 13 (2001) Rudd and Whelan (2005) ULC ULC ULC 1 ULC 8

14 p t nulc t = λ 1 (p t 1 nulc t 1 ) nulc t + (1 λ 1 )E t + φ 2 λ 1 E t j=0 λ j 2 (i t+j /y t+j ) + (1 λ 1 )κ j=0 λ j 2 nulc t+j (5) nulc ULC λ 1, λ 2 = 1{ 1+φ 0+φ 1 2 φ 1 ± [( 1+φ 0+φ 1 φ 1 ) 2 4 φ 1 ] 1/2 } κ = ln(1 α) MC 3 (5) ULC Sbordone (2002) [ nulc, p nulc] 2 VAR ULC 15 [ nulc, i/y, p nulc] 3 VAR(1) ULC 1617 3.2 1980 2005 SNA GDP 18 3 14 Sbordone (2002) Campbell and Shiller (1987) 15 Kurmann (2005) Sbordone (2002) 2 1 2 Sbordone (2005) 2 GMM Kurmann (2005) 16 4 (2004) Sbordone (2002) 17 β = 0.99 18 9

ULC ULC SNA / GDP /(+ ) 19 3.3 (ADF ) PP 1 (π) (i/y) ULC ( ulc) ULC (pulc) ADF PP 20 Sbordone (2002) ULC KPSS pulc pulc 4 3 95% (ξ) 1 4 4.1 4.1.1 ( 3 1 ) 95% R 2 19 HP 16000 P c = P I Greenwood, Hervowitz, and Krusell (1997) 20 PP ( 100) 10

0.88 21 4 4 Sbordone (2002) 4 VAR Sbordone (2002) Fuhrer and Moore (1995) Sbordone (2002) VAR 4.1.2 (η) (ɛ) (ɛ = 6.63, η = 27.99) 1.09 12.11 ( 4 1 ) 5 1.17 1.47 1 (ς) 0.71 3.44 1 22 NKPC 7 NKPC 0.52-0.58 Calvo NKPC (2002 ς 0.736-0.906 3.79-10.64 21 Sbordone (2002) NKPC (2004) R 2 0.9 22 1/(1 ς) = 1/(1 0.709514) 3.44 11

Gali and Gertler (1999) ς 0.829 5.85 (2000) 1 1-2 50% 20% 5 Taylor (1999) 1 23 NKPC φ 0 0.345 φ 2-0.014 24 NKPC (φ 0 ) 0.382 NKPC 7.43% 4.1.3 NKPC NKPC NKPC NKPC η = ɛ F F F 11.48 p 0.001 NKPC 1% 23 (2006) 4 24 φ 2 12

NKPC 4.2 GDP 3 2 Alt.π F 1 VAR 3 3 8 Sbordone (2002) 1 VAR VAR GDP (Z1) GDP (Z2) (Z3) 3 5 6 8 GDP VAR 4 1.05-1.13 2.48-3.44 80 5 13

5.1 (ξ) 2 (ξ/[ξ 1]) 2.5 5.2 6 NKPC 2 80 90 80 90 80 90 P t = ξ t ξ t 1 MC t markup t MC t P t = markup t + MC t (6) 7 (6) markup t 0.5% 14

7 IT 90 (2000) 1 2 5.3 NKPC NKPC 15

6 80 NKPC (2006) Calvo-Rotemberg (2006) Calvo (Dotsey, King, and Wolman (1999)) Calvo 25 25 Alvarez, Burriel, and Hernando (2005) Calvo 16

(1996) Nishimura, Ohkusa, and Ariga (1999) 26 27 NKPC NKPC NKPC 1 1 NKPC 8 1.1 1.1.1 CES (C t ) 26 (1996) 27 17

[ 1 C t = C t (z) ɛ 1 ɛ dz 0 ] ɛ ɛ 1 CES [ ] ɛ Pt (z) C t (z) = C t P c t [ 1 Pt c = P t (z) 1 ɛ dz 0 1.1.2 ] 1 1 ɛ E t i=0 β i {U(C t+i ) V (N t+i )} E U( ) V ( ) C N C t = W t Pt c N t + Z t K t + Π t (1/Rn t )B t B t 1 P c t Q t [K t+1 (1 δ)k t ] γ < 1 γ n > 0 W/P c Z t Π t B R n Q t δ 1.2 1.2.1 CES [ 1 ] η I t = I t (z) η 1 η 1 η dz 0 18

CES [ ] η Pt (z) I t (z) = I t P I t [ 1 Pt I = P t (z) 1 η dz 0 ] 1 1 η 1.2.2 input 28 ( ) It K t+1 = ϑ K t + (1 δ)k t K t ϑ ϑ ( ) > 0, ϑ ( ) 0, ϑ(0) = 0, ϑ(ī/ K) = Ī/ K ϑ [ ( ) ] } It max {Q t ϑ K t I t K t 1 ( ) Q t ϑ It = 1 K t ϑ(i t /K t )K t = I t 1.3 Y t (z) = K t (z) α N t (z) 1 α 28 Bernanke, Gertler, and Gilchrist (1999) Fukunaga (2002) 19

z (W t /P t ) (Z t ) [ ] Wt min N Pt c t (z) + Z t K t (z) subject to N t (z) 1 α K t (z) α Y t 0 (MC) MC t = W t /P c t (1 α)[y t (z)/n t (z)] = Z t α[y t (z)/k t (z)] Y t (z)/n t (z) = Y t /N t Y t (z)/k t (z) = Y t /K t ULC MC t = W t /Pt c (1 α)(y t /N t ) = 1 1 α ULC t P t (z) NKPC 2 Calvo NKPC (3) [ ˆp t (z) = (1 βς)e t (ςβ) j ˆmc t+j + ˆp c t+j j=0 ] (7) + 1 ɛ + ɛmc C ɛ CȲ + η ĪȲ 1 Ȳ ĉt+j(z) + 1 η + ηmc Ī ɛ CȲ + η ĪȲ 1 Ȳ ît+j(z) ˆp c t = ς ˆp c t 1 + (1 ς)ˆp t (z) ˆp I t = ς ˆp I t 1 + (1 ς)ˆp t (z) ˆp c 0 = ˆp I 0 ˆpc t = ˆp I t ˆp t for all t 20

C t+j (z) I t+j (z) E t E t j=0 j=0 (βς) j ĉ t+j (z) = ɛˆp t(z) 1 βς + E t (βς) j î t+j (z) = ηˆp t(z) 1 βς + E t (βς) j (ɛˆp t+j + ĉ t+j ) j=0 ( ) (βς) j ηˆp t+j + î t+j (7) 2 3 summation ˆp t (z) 29 ˆp t (z) ˆp t = 1 βς X [ j=0 ] ˆmc t + 1 ɛ + ɛmc C ɛ CȲ + η ĪȲ 1 Ȳ ĉt + 1 η + ηmc Ī ɛ CȲ + η ĪȲ 1 Ȳ ît + βς(e tˆp t+1 (z) ˆp t ) ˆp t (z) ˆp t (z) = 1 1 ς (ˆp t ς ˆp t 1 ) (8) (4) Calvo NKPC (8) 3: NKPC (4) ULC nulcp φ 0 (nulc t + κ) + φ 2 ( i t /y t ) = ˆp t φ 1 E t ˆp t+1 + φ 0ˆp t ( = φ 1 1 1 + φ 0 + φ 1 L 1 + 1 ) L 2 E tˆp t+1 φ 1 φ 1 = φ 1 (1 λ 1 L)(1 λ 2 L)E tˆp t+1 = φ 1 (λ 2 χ t χ t+1 ) 29 C t+j (z) I t+j (z) (7) 21

L λ 1, λ 2 1 [(1 + φ 0 + φ 1 )/φ 1 ]L 1 + (1/φ 1 )L 2 χ t+1 (1 λ 1 L)E tˆp t+1 χ χ t = 1 φ 1 λ 2 E t j=0 λ j 2 [ ] φ 0 (nulc t+j + κ) + φ 2 (i t+j /y t+j ) ˆp t (5) 4:Sbordone (2002) t Z t Z t = ΓZ t 1 + ɛ Zt (ɛ Z i.i.d.) Γ VAR E t Z t+i E t Z t+i = Γ i Z t t E t i=0 Z t+i = (I Γ) 1 Z t I (5) ɛ p ɛ p t [p t nulc t ] model [p t nulc t ] data ψ [p t nulc t ] model f(ψ) 30 ˆψ = argmin var(ɛ p t ) 30 Matlab optimization toolbox 22

1: ULC ( ) 2: GDP ( ) 23

3: ( ) ( ) GDP 24

1: (1): ADF PP ADF PP dulc -11.4663 *** -11.3701 *** (0.00) (0.00) i/y -2.10024 ** -2.58485 *** (0.03) (0.01) π -3.74709 *** -5.20703 *** (0.00) (0.00) pulc -2.902723 ** -2.4685 (0.05) (0.13) ( ) p 2: (2);KPSS dulc i/y π pulc KPSS 0.102277 0.093182 0.084745 0.097209 ( )KPSS 1%:0.216 5%:0.146 10%:0.119 25

3: (1) NKPC ɛ η ς R 2 F stat Baseline 6.628282 27.98906 0.709519 0.884365 11.47548 (5.614,7.643) (24.12,31.86) (0.614,0.805) 0.00102 Alt.π 9.553999 33.42204 0.659107 0.877363 5.672102 (7.977,11.13) (27.18,39.66) (0.584,0.735) 0.019189 Z1 (Baseline) 5.6022 23.43235 0.689467 0.871787 6.00359 (4.814,6.39) (20.54,26.32) (0.596,0.783) 0.016069 Z2 (Baseline) 5.892666 15.74376 0.597442 0.862374 12.96209 (5.349,6.437) (13.80,17.69) (0.563,0.632) 0.000503 Z3 (Baseline) 6.767318 32.19635 0.733032 0.885955 10.26346 (5.612,7.92) (27.72,36.66) (0.591,0.875) 0.001836 Z1 (Alt.π) 5.764054 24.10516 0.680043 0.846598 8.219541 (4.848,6.68) (20.75,27.46) (0.574,0.786) 0.005083 Z2 (Alt.π) 6.245166 16.44613 0.608448 0.845026 11.0425 (5.592,6.898) (14.11,18.78) (0.571,0.645) 0.001257 Z3 (Alt.π) 10.91452 47.39208 0.689428 0.875302 9.643931 (8.276,13.55) (36.75,58.03) (0.533,0.846) 0.002491 ( ) 95% F p F H 0 : ɛ = η ( )Alt.π GDP Z1 Z2 Z3 GDP π GDP π 4: (1) (ξ) Baseline 12.11 1.09 3.44 1.16 Alt.π 15.68 1.07 2.93 1.36 Z1 (Baseline) 10.18 1.11 3.22 1.24 Z2 (Baseline) 8.42 1.13 2.48 1.61 Z3 (Baseline) 13.29 1.08 3.75 1.07 Z1 (Alt.π) 10.47 1.11 3.13 1.28 Z2 (Alt.π) 8.86 1.13 2.55 1.57 Z3 (Alt.π) 20.28 1.05 3.22 1.24 26

4: : ( ) ( pt nulc t ) (p t nulc t ) R 2 = 0.88 ( ) 5: (1996) 1.41 Hall (1988) 1972-1992 IV Nishimura 1.17 1971-1994 et al (1999) 21 (2001) 1.47 1972-1995 (2004) 1.23 Roeger (1995) 1970-1998 22 27

6: (2):ɛ = η ς ξ R 2 Baseline 0.545929 8.561198 0.851704 (0.543,0.549) (8.484,8.638) Alt.π 0.563165 9.109829 0.834462 (0.56,0.566) (9.00,9.22) Z1 (Baseline) 0.530376 10.07066 0.858703 (0.528,0.533) (9.957,10.18) Z2 (Baseline) 0.53865 13.57812 0.877094 (0.536,0.540) (13.38,13.78) Z3 (Baseline) 0.556361 11.71394 0.874651 (0.554,0.559) (11.57,11.86) Z1 (Alt.π) 0.528331 10.74109 0.832035 (0.525,0.531) (10.58,10.90) Z2 (Alt.π) 0.54163 21.9664 0.869459 (0.539,0.543) (21.31,22.62) Z3 (Alt.π) 0.573827 17.08086 0.871964 (0.572,0.576) (16.70,17.47) 7: (2) (ξ) Baseline 8.56 1.13 2.20 1.82 Alt.π 9.11 1.12 2.29 1.75 Z1 (Baseline) 10.07 1.11 2.13 1.88 Z2 (Baseline) 13.58 1.08 2.17 1.85 Z3 (Baseline) 11.71 1.09 2.25 1.77 Z1 (Alt.π) 10.74 1.10 2.12 1.89 Z2 (Alt.π) 21.97 1.05 2.18 1.83 Z3 (Alt.π) 17.08 1.06 2.35 1.70 28

5: 1 ( 2000 ( ) (2000) ( ) 1,206( :630) 29

6: ( ) η = ɛ 7: ( ) 30

8: Firms Price Stickiness (monopolistic competition) Retailer Wholesaler investment goods (perfect competition) consumption goods (perfect competition) Capital Producer new capital (perfect competition) Household labor supply capital rental (perfect competition) 31

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Roberts, J. (1995): New-Keynesian Economics and the Phillips Curve, Journal of Money, Credit and Banking, 27, 975 984. Roeger, W. (1995): Can Imperfect Competition Explain the Difference between Primal and Dual Productivity Measures? Estimates for U.S. Manufacturing, Journal of Political Economy, 103, 316 330. Rotemberg, J. J. (1982): Sticky Prices in the United States, Journal of Political Economy, 90, 1187 1211. Rotemberg, J. J., and G. Saloner (1986): A Supergame-Theoretic Model of Business Cycles and Price Wars During Booms, American Economic Review, 76, 390 407. Rudd, J. and K. Whelan (2005): Does the Labor Share of Income Drive Inflation, Journal of Monetary Economics, 52, 1167 1181. Sbordone, A. M. (2002): Prices and unit labor costs: a new test of price stickiness, Journal of Monetary Economics, 49(2), 265 292. (2005): Do Expected Future Marginal Costs Drive Inflation Dynamics?, Journal of Monetary Economics, 52, 1183 1197. Taylor, J. B. (1999): Staggered Price and Wage Setting in Macroeconomics, in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, vol. 1B. Elsevier, New York. 34