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
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- ねんたろう ほうねん
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1 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 年 7 月 日 本 銀 行 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
2 NKPC NKPC JEL Classification: E31,E32 (toyoichirou.shirota@boj.or.jp) 1
3 1 (New Keynesian Phillips Curve, NKPC) NKPC NKPC NKPC 1 2 (2002) 90 1 (1) (2) 2 2
4 Kalecki (1938)Rotemberg and Saloner (1986) Bils (1985) Gali (1994) sluggishness NKPC 2 NKPC 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
5 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 > 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 > CES 4
6 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
![(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](/docs-images/43/23125399/images/page_6.jpg "(z)] (3) 2.")
7 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 (4) 1 2 NKPC
8 φ 2 (ɛ η) (ɛ < η) φ 2 (ξ t ) (ɛ > η) φ 2 (4) 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
9 E t π t+1 9 Gali and Gertler (1999) GMM Sbordone (2002) Campbell and Shiller (1987) VAR GMM 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
10 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 SNA GDP Sbordone (2002) Campbell and Shiller (1987) 15 Kurmann (2005) Sbordone (2002) Sbordone (2005) 2 GMM Kurmann (2005) 16 4 (2004) Sbordone (2002) 17 β =
![nulc, p nulc] 2 VAR ULC 15 [ nulc, i/y, p nulc] 3 VAR(1) ULC 1617 3.](/docs-images/43/23125399/images/page_10.jpg "2 1980 2005 SNA GDP 18 3 14 Sbordone (2002) Campbell and Shiller (1987) 15 Kurmann (2005) Sbordone (2002) 2 1 2 Sbordone (2005)")
11 ULC ULC SNA / GDP /(+ ) (ADF ) PP 1 (π) (i/y) ULC ( ulc) ULC (pulc) ADF PP 20 Sbordone (2002) ULC KPSS pulc pulc % (ξ) ( 3 1 ) 95% R 2 19 HP P c = P I Greenwood, Hervowitz, and Krusell (1997) 20 PP ( 100) 10
12 Sbordone (2002) 4 VAR Sbordone (2002) Fuhrer and Moore (1995) Sbordone (2002) VAR (η) (ɛ) (ɛ = 6.63, η = 27.99) ( 4 1 ) (ς) NKPC 7 NKPC Calvo NKPC (2002 ς Sbordone (2002) NKPC (2004) R /(1 ς) = 1/( )
13 Gali and Gertler (1999) ς (2000) % 20% 5 Taylor (1999) 1 23 NKPC φ φ NKPC (φ 0 ) NKPC 7.43% NKPC NKPC NKPC NKPC η = ɛ F F F p NKPC 1% 23 (2006) 4 24 φ 2 12
14 NKPC 4.2 GDP 3 2 Alt.π F 1 VAR Sbordone (2002) 1 VAR VAR GDP (Z1) GDP (Z2) (Z3) GDP VAR
15 5.1 (ξ) 2 (ξ/[ξ 1]) NKPC 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
16 7 IT 90 (2000) NKPC NKPC 15
17 6 80 NKPC (2006) Calvo-Rotemberg (2006) Calvo (Dotsey, King, and Wolman (1999)) Calvo Alvarez, Burriel, and Hernando (2005) Calvo 16
18 (1996) Nishimura, Ohkusa, and Ariga (1999) NKPC NKPC NKPC 1 1 NKPC CES (C t ) 26 (1996) 27 17
19 [ 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 ] 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 CES [ 1 ] η I t = I t (z) η 1 η 1 η dz 0 18
20 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 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
![= 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](/docs-images/43/23125399/images/page_20.jpg "t 1.3 Y t (z) = K t (z) α N t (z) 1 α 28 Bernanke, Gertler, and Gilchrist (1999)")
21 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
22 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 φ 0 + φ 1 L ) 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
23 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
24 1: ULC ( ) 2: GDP ( ) 23
25 3: ( ) ( ) GDP 24
26 1: (1): ADF PP ADF PP dulc *** *** (0.00) (0.00) i/y ** *** (0.03) (0.01) π *** *** (0.00) (0.00) pulc ** (0.05) (0.13) ( ) p 2: (2);KPSS dulc i/y π pulc KPSS ( )KPSS 1%: %: %:
27 3: (1) NKPC ɛ η ς R 2 F stat Baseline (5.614,7.643) (24.12,31.86) (0.614,0.805) Alt.π (7.977,11.13) (27.18,39.66) (0.584,0.735) Z1 (Baseline) (4.814,6.39) (20.54,26.32) (0.596,0.783) Z2 (Baseline) (5.349,6.437) (13.80,17.69) (0.563,0.632) Z3 (Baseline) (5.612,7.92) (27.72,36.66) (0.591,0.875) Z1 (Alt.π) (4.848,6.68) (20.75,27.46) (0.574,0.786) Z2 (Alt.π) (5.592,6.898) (14.11,18.78) (0.571,0.645) Z3 (Alt.π) (8.276,13.55) (36.75,58.03) (0.533,0.846) ( ) 95% F p F H 0 : ɛ = η ( )Alt.π GDP Z1 Z2 Z3 GDP π GDP π 4: (1) (ξ) Baseline Alt.π Z1 (Baseline) Z2 (Baseline) Z3 (Baseline) Z1 (Alt.π) Z2 (Alt.π) Z3 (Alt.π)
28 4: : ( ) ( pt nulc t ) (p t nulc t ) R 2 = 0.88 ( ) 5: (1996) 1.41 Hall (1988) IV Nishimura et al (1999) 21 (2001) (2004) 1.23 Roeger (1995)
29 6: (2):ɛ = η ς ξ R 2 Baseline (0.543,0.549) (8.484,8.638) Alt.π (0.56,0.566) (9.00,9.22) Z1 (Baseline) (0.528,0.533) (9.957,10.18) Z2 (Baseline) (0.536,0.540) (13.38,13.78) Z3 (Baseline) (0.554,0.559) (11.57,11.86) Z1 (Alt.π) (0.525,0.531) (10.58,10.90) Z2 (Alt.π) (0.539,0.543) (21.31,22.62) Z3 (Alt.π) (0.572,0.576) (16.70,17.47) 7: (2) (ξ) Baseline Alt.π Z1 (Baseline) Z2 (Baseline) Z3 (Baseline) Z1 (Alt.π) Z2 (Alt.π) Z3 (Alt.π)
30 5: 1 ( 2000 ( ) (2000) ( ) 1,206( :630) 29
31 6: ( ) η = ɛ 7: ( ) 30
32 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
33 (1996):, 38, (2005): TFP 1990, 176, (2005): 05-J-8. (2006): 06-J-02. (2001): TFP, 52, (2000):. (1996):, (2004): 04-J-11. (2002):, Alvarez, L. J., P. Burriel, and I. Hernando (2005): Do Decreasing Hazard Functions for Price Changes Make Any Sense?, Working paper Series No.461, European Central Bank. Bernanke, B., M. Gertler, and S. Gilchrist (1999): The Financial Accelerator in a Qunatitative Business Cycle Framework, in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, vol. 1C. Elsevier, New York. Bils, M. (1985): Pricing in a Customer Market, Quarterly Journal of Economics, 104, Calvo, G. A. (1983): Staggered Prices in a utility-maximizing framework, Journal of Monetary Economics, 12,
34 Campbell, Y., and R. Shiller (1987): Cointegration and Test of Present Value Models, Journal of Political Economy, 95, Chari, V., P. Kehoe, and E. McGrattan (2000): Sticky Price Model of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?, Econometrica, 68, Dotsey, M., R. King, and A. Wolman (1999): State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output, Quarterly Journal of Economics, 114, Fuhrer, J. C. and G. Moore (1995): Inflation Persistence, Quarterly Journal of Economics, 110, Fukunaga, I. (2002): Financial Accelerator Effects in Japan s Business Cycle, Working paper Series 02-06, Bank of Japan. Gali, J. (1994): Monopolistic Competition, Business Cycles, and the Composition of Aggregate Demand, Journal of Economic Theory, 63(1), Gali, J., and M. Gertler (1999): Inflation Dynamics: A Structural Econometric Analysis, Journal of Monetary Economics, 44(2), Greenwood, J., Z. Hervowitz, and P. Krusell (1997): Long-Run Implication of Investment-Specific Technological Change, American Economic Review, 87, Hall, R. (1988): The relation between Price and Marginal Cost in U.S. Industry, Journal of Political Economy, 96, Kalecki, M. (1938): The Determinants of the Distribution of National Income, Econometrica, 6, Kiley, M. (1997): Staggered Price Setting and Real Rigidities, Working paper Series 97-46, Federal Reserve Board. Kurmann, A. (2005): Quantifying the uncertainty about a forwardlooking New Keynesian pricing model, Journal of Monetary Economics, 52, Nishimura, K., Y. Ohkusa, and K. Ariga (1999): Estimating the Mark-up over Marginal Cost: a Panel Analysis of Japanese Firms , International Journal of Industrial Organization, 17,
35 Roberts, J. (1995): New-Keynesian Economics and the Phillips Curve, Journal of Money, Credit and Banking, 27, 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, Rotemberg, J. J. (1982): Sticky Prices in the United States, Journal of Political Economy, 90, Rotemberg, J. J., and G. Saloner (1986): A Supergame-Theoretic Model of Business Cycles and Price Wars During Booms, American Economic Review, 76, Rudd, J. and K. Whelan (2005): Does the Labor Share of Income Drive Inflation, Journal of Monetary Economics, 52, Sbordone, A. M. (2002): Prices and unit labor costs: a new test of price stickiness, Journal of Monetary Economics, 49(2), (2005): Do Expected Future Marginal Costs Drive Inflation Dynamics?, Journal of Monetary Economics, 52, 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
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