Hsiao (2003, 6 ) Maddala, Li, Trost and Joutz (1997) Hsiao and Pesaran (2004) 4.2 y it = γy it 1 + x itβ + ε it i = 1, 2,..., N t = 1, 2,...T (
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1 Balestra and Nerlove (1966) (GMM) Arellano and Bond (1991) Arellano (2003) N T N T Smith and Fuerter (2004) 1 (the random coefficient model) Singer and Willett ( ) 2004)
2 Hsiao (2003, 6 ) Maddala, Li, Trost and Joutz (1997) Hsiao and Pesaran (2004) 4.2 y it = γy it 1 + x itβ + ε it i = 1, 2,..., N t = 1, 2,...T (1) γ x it K β K ε it ε it = µ i + u it (2) µ i iidn(0, σµ) 2, u it iidn(0, σu) 2 ε it N T 2 u it Maddala (2001) y it = x itβ + µ i + w it (3) w it = ρw it 1 + u it ρ < 1 (4) y it = γy it 1 + x itβ + µ i + u it (5) 2
3 Lillard and Willis (1978) AR(1) Lillard and Weiss (1979) Baltagi and Li (1991) Wansbeek (1992) (4) the Paris-Winsten (PW) transformation Maddala(2001) Nerlove(( ) (3) LSDV ŵ it 4) OLS ˆρ 3) y it = x itβ + µ i + u it (6) y it = y it ˆρy it 1 x it = x it ˆρx it 1 µ i = µ i (1 ˆρ) LSDV β µ i Bhargava, Franizini and Narendranathan (1982) Durbin-Watson Statistic w it = ρw it 1 + u it H 0 : ρ = 0 H 1 : ρ < 1 N T i=1 t=2 d = (ŵ wit ŵ wit 1 ) 2 N T i=1 t=1ŵ2 wit (7) û wit AR(1) AR(n) Baltagi and Li (1995) AR(1) AR(1) AR(1)
4 AR(1) MA(1) Balestra and Nerlove(1966) OLS Maddala (1971a, 1971b) Nickell (1981) (GMM) Maddala (2001) 4 Sevestre and Trognon (1996, pp ) Maddala (1971a) λ λ class β = 0 γ(λ) p lim ˆγ(0) < γ < p lim ˆγ(λ) < p lim ˆγ(1) < p within GLS poolingols lim between ˆγ( ) (8) GLS 3 Baltagi and Li (1995) Baltagi (2001,pp.90-95) (survival analysis)
5 Ridder and Wansbeek (1990, pp ) Trognon(1978) AR(1) x it = δx it 1 + w it w it N(0, σ 2 w) y i0 T γ Anderson and Hsiao (1981,1982) 4.3 Anderson and Hsiao (1981,1982) w it = γw it 1 + ρ z i + β x it + µ i + u it i = 1, 2,..N. t = 1, 2,...T (9) y it = w it + η i (10) µ i = (1 γ)η i E(η i ) = 0 V ar(η i ) = σ 2 η = σ 2 µ/(1 γ) 2 (11) z i 1 y i0 (µ i +ρ z i )/(1 γ) + β j=0 x it jγ j µ i y i0 y i0 µ i y i0 y i1 y i1... µ i 2 y i0 µ i u it y i0 = ȳ 0 + ε i ȳ 0 0 ε i iid ( 2a y i0 µ i ( 2b)y i0 µ i cov(y i0, µ i ) = ϕσy 2 0 y it [ϕε i /(1 γ)] = lim t E[y it ρ z i /(1 γ) β t 1 j=0 x it jγ j ε i ] 3 w i0 y it = w it + η i µ i = (1 γ)η i y it µ i y i0 η i + ρ z i /(1 γ) + β t 1 j=0 x it jγ j
6 w i0 3 w it 4 ( 4a)w i0 θ w σu/(1 2 γ 2 ) ( 4b)w i0 θ w σw 2 0 ( 4c)w i0 θ i0 σu/(1 2 γ 2 ) ( 4d)w i0 θ i0 σw0 2 Anderson and Hsiao (1981,1982) 8 5 L(γ, ρ, β, γ, η, σ 2 u, σ 2 w, σ 2 µ) = (2π) NT/2 v N/2 exp{ 1 2σ 2 (y it γy it 1 ρ z i β x it ) 2 } i t (12) v N T σ 2 µ = 0 Anderson and Hsiao (1981) (9) 10 z i µ i y it y it 1 = (x it x it 1 ) β + γ(y it 1 y it 2 ) + (u it u it 1 ) (13) u it 6 β γ 7 (y it 2 y it 3 ) 5 Anderson and Hsiao (1982) Hisao ( ) 6 y it 1 u it Hsiao (2003, pp.85-86)
7 ( γ iv β iv ) [ ( N T (y i,t 1 y i,t 2 )(y it 2 y it 3 ) (y it 2 y it 3 )(x it x it 1 ) ) = (x it x it 1 )(y it 2 y it 3 ) (x it x it 1 )(x it x it 1 ) i=1t=3 [ ( N T i=1t=3 (14) ) ] y it 2 y it 3 (y it y it 1 ) x it x it 1 )] 1 y it 2 ( γ iv β iv ) [ ( N T y it 2 (y i,t 1 y i,t 2 ) y it 2 (x it x it 1 ) ) = (x it x it 1 )y it 2 (x it x it 1 )(x it x it 1 ) i=1t=2 [ ( ) ] N T y it 2 (y it y it 1 ) i=1t=2 x it x it 1 )] 1 (15) (y i,t 1 y i,t 2 ) (y it 2 y it 3 ) y it ˆβ ˆγ 9 ρ ȳ it ˆγȳ it 1 ˆβ x it = ρ z i + µ i + ū it i = 1,..N (16) ȳ i = T t=1 y it/t, x i = T t=1 x it/t, ū i = T t=1 u it/t 3 σ 2 u σ2 µ N T σu 2 i=1 t=2 = it y it 1 ) ˆγ(y it 1 y it 2 ) ˆβ (x it x it 1 )] 2 2N(T 1) (17) N σµ 2 i=1 = i ˆγȳ i, 1 ˆρ z i ˆβ x i ) 1 N T ˆσ2 u (18) N T γ β σ 2 u ρ σµ 2 N N T Anderson and Hsiao (1982) N T T N 8 8 Arellano (1989) y it 2 y it 3 (y it 2 y it 3 )
8 γ 3 T N ρ N T 3 T N ρ N T γ ρ γ N T ( 3) T N T N Hsiao, Pesaran and Tahmiscioglu (2002) Fujiki, Hsiao and Shen (2002) Chamberlain (1982,1984) (Minimum Distance Estimation: MDE) 9 2 (β, γ) min[ N u i=1 i Ω 1 u i ] (19) Ω u i u i = [ y i1 β x i1 γ y i0, y i2 β x i2 γ y i1,...] N 4.4 Arellano and Bond (1991) Ahn and Schmidt (1995) 2 y 10 E[y is, (u it u i,t 1 )] = 0, s = 0, 1,...t 2, t = 2,...T (20) Arellano and Bond (1991) GMM) 1 n i=1 n y is[(y it y i,t 1 ) (y i,t 1 y i,t 2 ) γ (x it x i,t 1 ) β] = 0 (21) s = 0,..., t 2, t = 2,..., T 9 MDE Chamberlain (1982,1984) Lee(2002, 3 ) 10 Holtz-Eakin(1988) Holtz-Eakin, Newey and Rosen(1988)
9 (y i1, y i2, y i3,...y it 2 ) 11 [y i1 ] W i = 0 [y i1, y i2 ] (22) [y i1,...y it 2 ] 20) E(W i u i ) = 0 (23) 1 (y it y it 1 ) = (y it 1 y it 2 ) γ + (x it x it 1 ) β + (u it u it 1 ) (24) y it = y it 1γ+ x itβ+ u it i = 1, 2...N W i Arellano and Bond (1991) (GMM) (24) W y it = W y it 1γ + W x itβ + W u it (25) γ β ˆγ GMM = [( y it 1 ) W ˆβ GMM = [( x it 1 ) W 1 ˆV N W ( y it 1 )] 1 [( y it 1 ) 1 W ˆV N W ( y it )] (26) 1 ˆV N W ( x it 1 )] 1 [( x it 1 ) 1 W ˆV N W ( y it )] (27) V N = N i=1 W i ( u i)( u i ) W i 12 x it E(x it u is ) = 0, t, s = 1, 2,..., T x it µ i 24) x it x it (predetermined) E(x it u is ) 0 for s < t E(x it u is ) = 0 for s t (x i1, x i2,..., x is 1 ) W i 11 Baltagi (2001, p Arellano and Bond (1991, p.279) 25) one-step GMM two-step iid
10 Arellano and Bond (1991) GMM GMM Arellano and Bond (1991) j 13 1 r j = T 3 j T t=4+j r tj (28) r tj = E( u it u it j ) H 0 : r j = 0 m j = ˆr j SE(ˆr j ) (29) ˆr j û it ˆr tj = N 1 N i=1 û it û it j Arellano and Bond (1991) Sargan (1958) s = û W [ N i=1 W i ( û i )( û i ) W i ] 1 W ( û) χ 2 p k 1 (30) p W û 25) Arellano and Bond (1991) Ahn and Schmidt(1995) y y (u it u it 1 ) () E(y is u it ) = 0 t = 2,...T, s = 0, 1,...t 2 (31) E(u it u it ) = 0 t = 2,...T 1 (32) T (T 1)/2 + (T 2) (32) γ 1 σµ/σ 2 u 2 Ahn and Schmidt(1995) (31)(32) 1 i t cov(u it, y i0 ) cov(u it, y i0 ) = 0 13 Arellano (2003, pp )
11 i t cov(u it, µ i ) cov(u it, µ i ) = 0 3 i t s cov(u it, u is ) cov(u it, u is ) = GMM Chamberlain (1982,1984) (Minimum Distance Estomator) Blundell and Bond (1998) GMM GMM Anderson and Hsiao (1981,1982) GMM GMM Arellano and Bond GMM γ 1 µ i Blundell and Bond (1998) T=3 E(y i1 u i3 ) = 0 γ GMM y i2 = πy i1 + µ i + u i2 i = 1, 2,...N (33) γ 1 µ i π 0 y i1 y i2 E(y i1 µ i ) > 0 σ 2 µ = var(µ i ) σ 2 u = var(u it ) π k p lim ˆπ = (γ 1) (σµ/σ 2 u) 2 + k k = (1 γ) (1 + γ) (34) Blundell and Bond (1998) GMM Nelson amd Startz (1990) Staiger and Stock (1997) Ahn and Schumidt (1995) T-3 E(u it y it 1 ) = 0 t = 4, 5,...T (35) y i2 E(u i3 y i2 ) = 0 (36) y i y i0 y i0 t
12 y i1 = µ i 1 γ + u i1 (37) t = 2 y it (36) E[(µ i + u i3 )(u i2 + (γ 1)u i1 )] = 0 (38) E(u i1 µ i ) = E(u i1 u i3 ) = 0 i = 1, 2,...N (39) y i0 u i1 µ i /(1 γ) Blundell and Bond (1998) γ 1 σ µ/σ 2 u 2 (35)(36) GMM GMM Z + i GMM Z i y i Z + i = 0 0 y i (40) y it 1 Z i (T-2) m GMM y i Z i = 0 y i1 y i (41) y i1... y it 2 GMM σµ/σ 2 u 2 = 1, T = 4 GMM GMM γ = γ = γ = γ GMM GMM γ 1 σµ/σ 2 u 2
13 (GMM) GMM (OLS) GLS) (IV) (MDE) GMM GMM GMM Blundell and Bond (1998) GMM empirical likelihood empirical likelihood Owen (2001) Mittelhammer, Judge and Miller (2000) 16 STATA Johnston and DiNardo (
14 GMM Arellano and Bond (1991) N=100 T= GMM 2 GMM (IV) 3 two-step GMM Ziliak (1997) Ziliak (1997) N=532 T=8 iid GMM Keane and Runkle (1992) forward filter 2SLS(FF) 18 Ahn and Schmidt (1999) Crepon, Kramarz and Trognon (1997) Alonso-Borrego and Arellano (1999) N=100 T=4, GMM Alvarez and Arellano (2003) one-step GMM (LIML) N T 17 seed STATA seed Hayashi and Sims (1983) forward filtering
15 T/N 1/T 1/N 1/(2N-T) T GMM LIML T LIML GMM Blundell and Bond (1998) GMM N=100,200,500 T=4 GMM Binder, Hsiao, and Pesaran (2000) Hsiao, Pesaran and Tahmiscioglu (2002) Hsiao (2003) GMM GMM T=5 N=50, % GMM 15-20% GMM MDE GMM MDE GMM Hahn, Hausman and Kuersteiner (2002) 3 y n y n 3 (long differences;ld) Wansbeek and Bekker (1996) GMM Ahn and Schmidt (1995) Alvarez and Arellano (2003) T N T/N N/T N T
16 Frankel and Rose (1996) Pedroni(2001) Sala-i-Martin (1996) Nerlove (2000) Quah (1996) 2 Nagahata, Saita, Sekine and Tachibana (2004) spurious Levin-Lin (LL) test(1992,1993) Im-Pesaran-Shin (IPS) test(2003) Maddala-Wu (MW) test (1999) y it = γy it 1 + u it i = 1, 2,...N (42) t H 0 : γ 1 = 1 vs H 1 : γ 1 < 1 (43) Levin-Lin (LL) test H 0 : γ 1 = γ 2 =... = γ N = γ = 1 vs H 1 : γ 1 = γ 2 =... = γ N = γ < 1 (44)
17 O Connell(1998) Levin-Lin test Im-Pesaran-Shin (IPS) test Levin-Lin test H 0 : γ i = 1 for all i vs H 1 : γ i < 1 at least one i Maddala (2001, p.554) N Levin-Lin test Augmented Dickey-Fuller test N t M σ 2 t t M σ 2 /N Maddala-Wu test N Ronald A. Fisher (1973a) P i i p λ = 2 N i=1 log e P i 2N χ N P λ test Maddala and Wu (1999) Fisher Choi(1999) Fisher Fisher 4.7 STATA Wooldridge (2003) ( msu.edu/ ec/wooldridge/book2.htm) WAGEPAN.DTA Vella and Verbeek (1998) Wooldridge (2003) ln wage it = α + γ ln wage it 1 + β exp er it + δ exp er 2 it + ζhours it + ηhours it 1 + θunion i + κeduc i + λmarried i + νpoorhlth i + µ i + ν t + u it
18 ln wage = exp er = hours = union = 1 educ = married = 1 poorhlth = 1 ν t = STATA /**Dynamic Panel **/ /*Pooled OLS*/ reg lwage lwage 1 d81 d82 d83 d84 d85 d86 d87 exper expersq hours hours 1 union educ married poorhlth /*LSDV*/ xtreg lwage lwage 1 d81 d82 d83 d84 d85 d86 d87 exper expersq hours hours 1 union educ married poorhlth, fe est store fixed xtreg lwage lwage 1 d81 d82 d83 d84 d85 d86 d87 exper expersq hours hours 1 union educ married poorhlth, re xttest0 est store random hausman fixed random /*Anderson-Hsiao IV Estimation*/ xtivreg lwage lwage 1 d81 d82 d83 d84 d85 d86 exper expersq ( hours hours 1 = union educ married poorhlth ), re ec2sls /*Anderson-Hsiao Maximum Likelihood Estimation*/ xtreg lwage lwage 1 d81 d82 d83 d84 d85 d86 d87 exper expersq hours hours 1 union educ married poorhlth, mle /*Arellano-Bond GMM Estimation*/ xtabond lwage hours hours 1 d81 d82 d83 d84 d85 d86 d87, lags(1) inst(exper expersq union educ married poorhlth) artests(2) xtabond lwage hours hours 1 d81 d82 d83 d84 d85 d86 d87, lags(1) inst(exper expersq union educ married poorhlth) artests(2) robust
19 OLS γ F E(0.092) < MLE(0.17) < RE(0.49) = OLS(0.49) (IV) one-step GMM γ GMM IV GMM(0.31) < IV (0.57)
20
21 Dependent Variable: lwage Estimated Coefficient Pool OLS t-statistics Estimated Coefficient t-statistics Estimated Coefficient z-statistics Estimated Coefficient z-statistics lwage_ d d d d d d d (dropped) exper expersq hours hours_ union educ (dropped) married poorhlth _cons Fixed Random MLE Diagnostic Test Number of observation Number of groups (ari) R-sq: within between overall Log Likelihood F test that all u_i=0: sigma_u sigma_e rho Breusch and Pagan Lagrangian multiplier test for random effects: Hausman specification test Likelihood-ratio test of sigma_u = 0 for MLE F(544, 3757) = 6.19 Prob>F = chi2(1) = Prob > chi2 = chi2(13) = chibar2(01) = Prob>chibar2 =
22 Dependent Variable: lwage Estimated Coefficient z-statistics hours hours_ lwage_ d d d d d d exper expersq _cons Diagnostic Test Number of observation Number of groups R-sq: Wald test sigma_u sigma_e rho within between overall IV chi2(11) = Prob>chi2 = hours hours_1 lwage_1 d81 d82 d83 d84 d85 d86 exper Baltagi(2001) the error component two-stage least square (EC2SLS)
23 Dependent Variable: lwage one-step results Estimated Coefficient Robust z-statistics lwage_ hours hours_ d d d d d _cons Diagnostic Test Number of observation Number of groups Sargan test Wald test Arellano-Bond test for residual AR(1) Arellano-Bond test for residual AR(2) GMM chi2(26) = Prob>chi2 = chi2(8) = z = Prob>z = z = 2.20 Prob>z =
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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パネル・データの分析
パネル データの分析 内容 パネル データとは pooled cross section data の分析 パネルデータの分析 DID (Difference in Differences) モデル パネル データの分析 階差モデル (first difference model) fixed effects model random effects model パネル分析の実際 データ セットの作成
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TS001 Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestimation 49 mwp-055 corrgram/ac/pac 56 mwp-009 dfgls
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solutionJIS.dvi
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18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
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オーストラリア研究紀要 ３６号（Ｐ）☆／３．橋本
36 p.9 202010 Tourism Demand and the per capita GDP : Evidence from Australia Keiji Hashimoto Otemon Gakuin University Abstract Using Australian quarterly data1981: 2 2009: 4some time-series econometrics
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Analysis of Variance 2 two sample t test analysis of variance (ANOVA) CO 3 3 1 EFV1 µ 1 µ 2 µ 3 H 0 H 0 : µ 1 = µ 2 = µ 3 H A : Group 1 Group 2.. Group k population mean µ 1 µ µ κ SD σ 1 σ σ κ sample mean
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1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.
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ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
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seminar0220a.dvi
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7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
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7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α