2004 2 µ i ν it IN(0, σ 2 ) 1 i ȳ i = β x i + µ i + ν i (2) 12 y it ȳ i = β(x it x i ) + (ν it ν i ) (3) 3 β 1 µ i µ i = ȳ i β x i (4) (least square d

2004 1 3 3.1 1 5 1 2 3.2 1 α = 0, λ t = 0 y it = βx it + µ i + ν it (1) 1 (1995)1998Fujiki and Kitamura (1995).

2004 2 µ i ν it IN(0, σ 2 ) 1 i ȳ i = β x i + µ i + ν i (2) 12 y it ȳ i = β(x it x i ) + (ν it ν i ) (3) 3 β 1 µ i µ i = ȳ i β x i (4) (least square dummy variables: LSDV) N µ i T LSDV T N β µ i 2 3 x ỹ x = 1 N x it T N t=1i=1 (5) ỹ = 1 N y it T N (6) t=1i=1 x y S pool xx S pool xy S pool yy = N = N = N (x it x) 2 (7) (x it x)(y it ỹ) 2 (8) (y it ỹ) 2 (9) 2 3 Greene (2003, Chapter 13), pp.289-90

2004 3 () x i = 1 x it T t (10) ȳ i = 1 y it T (11) x S with xx S with xy S with yy = N = N = N t (x it x i ) 2 (12) (x it x i )(y it ȳ i ) (13) (y it ȳ i ) 2 (14) S btw xx S btw xy S btw yy = N T ( x it x) 2 (15) i=1 = N T ( x it x)(ȳ i ỹ) (16) i=1 = N T (ȳ i ỹ) 2 (17) i=1 S pool xx S pool xy S pool yy = S with xx = S with xy = S with yy + S btw xx (18) + S btw xy (19) + S btw yy (20) β β pool β with β btw β pool = [Sxx pool ] 1 Sxy pool = [Sxx with + Sxx btw ] 1 [Sxy with + Sxy btw ] (21) β with = [Sxx with ] 1 Sxy with (22) β btw = [S btw xx ] 1 S btw xy (23)

2004 4 S with xy S btw xy (21) = S with xx β with (24) = S btw xx β btw (25) β pool = m with β with + m btw β btw (26) m with = [S with xx + S btw xx ] 1 S btw xx = I m btw (27) (23) m with 3.3 N µ i µ i IID0σ µ 2 N 4 µ i µ i u it µ i IID(0, σµ) 2 (28) u it IID(0, σu) 2 (29) µ i v it = µ i + u it var(v it ) = σu 2 + σµ 2 cov(v it, v is ) = σµ 2 for t s cov(v it, v js ) = 0 for t, s if i j 4

2004 5 µ i u it generalized least square: GLS Maddala (1971a,b) 5 F with = (22)23 β rnd GLS = F β with + (1 F )β btw (30) S with xx Sxx with+θsbtw xx, θ = σ2 u σ 2 u +T σ2 µ β with = Swith xy Sxx with β btw = Sbtw xy Sxx btw (31) (32) 30 βgls rnd = Swith xy Sxx with + θs btw xy + θs btw xx (33) GLS LSDVOLSθ = 1 σ 2 µ = 0 LSDVθ = 0 σ 2 u = 0 OLSθ LSDV OLS 3.4 (heteroskedasticity) (heterogeneity) Mazodier and Trognon (1978) Baltagi (2001, Chapter 5) µ i u it Mazodier and Trognon (1978) µ i 5 Greene (2003, Chapter 13), pp.295-6

2004 6 Baltagi (2001, Chapter 5) u it [y it (1 θ i )ȳ i ] OLS θ i = σ 2 v σ 2 v + T σ 2 µ i (34) T t=1û2 it T K (35) θ i (feasible generalized least square estimation: FGLS) White(1980) heteroscedasticity consisitent estimation (autocorrelation) 4 3.5 6 6

2004 7 3.5.1 Neymaa, Jerzy (Peason, Egon. S. ) 7 8 910 1% 5% 10% 3 α n 7 Neyman and Pearson (1928a,b) 10 8 Lehmann(1986) 9 10

2004 8 11 µ n β 20-30% 12 3.5.2 LSDVOLS) F F (Lagrange Multiplier test) OLS 11 1 β power µ 12 90 75 20 75

2004 9 GLS Hausman test 3.1 3.1 3.5.3 F RSS 0 (ν 0 ) (RSS 1 ) (ν 1 ) ν 0, ν 1 F (ν 0, ν 1 ) = RSS 0/ν 0 RSS 1 /ν 1 (36) (N 1)(K + 1) (NT N(K + 1)) F K F (pool vs time series) = (RSS pool RSS T imeseries )/(N 1)(K + 1) RSS T imeseries /(NT N(K + 1)) (37) RSS pool RSS T imeseries F F

2004 10 F (oneway fixed vs time series) = (RSS of RSS T imeseries )/(N 1) RSS T imeseries /(N(T 1)K) (38) RSS of (N 1)NT (N + 1) F F (pool vs oneway fixed) = (RSS pool RSS of )/(N 1) RSS of /(NT (N + 1)) (39) F (T 1) (NT (N + 1)) (T 1)) F (oneway fixed vs twoway fixed) = (RSS of RSS tf )/(T 1) RSS tf /(NT (N + 1) (T 1)) (40) RSS tf F () 3.5.4 H 0 H 1 13 y = βx + u (41) 13 Maddala(2001pp.494-495

2004 11 OLS x u H 0 : x u H 1 : x u β β 0 H 0 H 1 β 1 H 0 H 1 H 0 q = β 1 β 0 Hausman 14 var( q) = var( β 1 ) var( β 0 ) H 0 V ( q) var( q) H 0 m = q2 V ( q) χ2 (1) (42) H 0 : x it H 1 : x it H 0 β r β f q = β f β r V (q) = V ( β f ) V ( β r ) m = q [ V ( q)] 1 q χ 2 (k) β k 1 V 1 V 0 m = q [ V( q)] 1 q χ 2 (k) (43) 15 14 var(ˆq) = var( ˆβ 1 ) var( ˆβ 0 ) cov( ˆβ 0, ˆq) = 0 Maddala(2001, pp.495-496) 15 k β

2004 12 3.5.5 Breusch-Pagan Breusch-Pagan µ µ i i y it = µ + x it β+u it (44) û it ( S 1 = N ) 2 û it (45) t=1 i=1 S 2 = N û 2 it (46) Lagrange Multiplier (LM) LM = NT ( ) 2 S1 1 χ 2 (1) (47) 2(T 1) S 2 Breusch-Pagan 3.6 3.6.1

2004 13 (weighted least square=wls) (self-selection reasons) 16 ANOVA() 17 18 ANOVA Townsend and Searle (1971) Baltagi and Chang (1994) ANOVA ANOVA (variance component ratio) 19 16 (New Jersey) Gary Hausman and Wise (1979) 17 ANOVA (Searle (1971)Townsend and Searle (1971)Wallace and Hussain (1969)Swamy and Arora (1972)Fuller and Battese (1974)Henderson (1953) 18 Jennrich and Sampson (1976)Harville (1977)Das (1979)Corbeil and Searle (1976a,b)Hocking (1985) 19

2004 14 (rotating panel 6 6 1 6 5 6 1 ( ) 3.2 2 incidental truncation problemheckman ( ) 3.6.2 (FGLS) σv λ i 1 2 σv 2 + T i σµ 2 (48) i y it λ i ȳ i = (x it λ i x i ) β + ε it (49) 20 20 Wooldridge(2002, chap17), pp.578-580

2004 15 y it = x itβ + µ i + u it t = 1,..., T (50) x it 1 k β k 1 µ i x it i t = 1 i i s i (s i1,..., s it ) T 1 selection indicators) (x it, y it ) s it = 1 s it = 0 {(x i, y i, s i ) : i = 1, 2,..., N} s i i (1) β ˆβ = ( N 1 N = β + ) 1 ( ) s it ẍ itẍ it N 1 N s it ẍ itÿ it ( N 1 N ) 1 ( ) s it ẍ itẍ it N 1 N s it ẍ itu it (51) ẍ it x it T 1 i s ir x ir, r=1 ÿ it y it T 1 i s ir y ir, r=1 T i T s it t=1 t E(S it ẍ it u it) = 0 ẍ it x i s i (a) E(u it x i, s i, µ i ) = 0 t = 1, 2,..., T (b) T t=1 E(s it ẍ itẍit) (c) E(u i u i x i, s i, µ i ) = σui 2 T (a) (b) s i (u i, x i, µ i ) E(u it x i, µ i ) s i µ i s i µ i E(µ i x i ) = 0 (c) (a),(c)

2004 16 ( ) [ ] V ar s it ẍ itu it = σu 2 E(s it ẍ itẍ it ) t=1 t=1 (52) ˆσ 2 u ( N ˆσ 2 u ) 1 s it ẍ itẍ it (53) ( ) ( ) E s it ü 2 it = E s it E(ü 2 it s i ) = E { [ ]} T i σ 2 u (1 1T i = σ 2 u E [(T i 1)] t=1 t=1 (54) s it = 1 û it = ÿ it ẍ it ˆβ N 1 N (T i 1) p E(T i 1) i=1 [ ] ˆσ u 2 = N 1 N 1 (T i 1) N 1 N i=1 plim ˆσ u 2 = σu 2 N [ N s it û 2 it = (T i 1) i=1 ] 1 N s it û 2 it (55) 3.7 STATA ln Y it = α 0 + α ln K it + β ln L it + γdebt/asset it + δ(debt/asset) 2 it (56) + ζ(own capital ratio) it + η(sales share) it + ε it (TFP) 21 21

2004 17 7 ln Y it = ln rsln K it = ln k ln L it = ln Ldebt/asset it = darat(debt/asset) 2 it = darat2 2 (own capital ratio) it = ocaprat (sales share) it = ssuriagesyea STATA xtreg lnrs lnk lnl darat darat2 ocaprat ss, i(arin) fe xtreg lnrs lnk lnl darat darat2 ocaprat ss, i(arin) re xttest0 hausman STATA fe re Breusch-Pagan xttest0 hausman ( arin ) i(arin) 3.3 26195 33 1.027 1 Breusch-Pagan STATA

Hausman Test LM Test F Test Hausman Test F Test LM Test F Test F Test

3.2

Estimated Coefficient t-statistics Estimated Coefficient z-statistics Ink 0.1637300 50.09 0.1641548 50.24 InL 0.8635048 151.85 0.8632702 151.88 darat -0.5927591-9.42-0.5957934-9.47 darat2-0.0163443-4.51-0.0163759-4.52 ocaprat -0.7173559-11.87-0.7204153-11.92 ss 7.5123060 22.67 7.4631300 22.61 _cons -0.0698154-1.01-0.4007013-4.54 Diagnostic Test Number of observation Number of groups R-sq: Dependent Variable: Inrs within between overall F test that all u_i=0: sigma_u sigma_e rho Breusch and Pagan Lagrangian multiplier test for random effects: Hausman specification test Fixed Random 26195 26915 33 33 0.7299 0.7299 0.4554 0.4564 0.6123 0.6124 F(32, 26156) = 527.74 Prob>F = 0.0000 0.3940 0.6337 0.2788 0.3103 0.6337 0.1934 chi2(1) = 1.1e + 07 Prob > chi2 = 0.0000 chi2(6) = 22.06 Prob>chi2 = 0.0012