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

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1 α = 0, λ t = 0 y it = βx it + µ i + ν it (1) 1 (1995)1998Fujiki and Kitamura (1995).

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

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 =

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)

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 =

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

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

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

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.

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)

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

8 µ n β 20-30% LSDVOLS) F F (Lagrange Multiplier test) OLS 11 1 β power µ

9 GLS Hausman test 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

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 () H 0 H 1 13 y = βx + u (41) 13 Maddala(2001pp

(N + 1)) (39) F (T 1) (NT (N + 1)) (T 1)) F (oneway fixed vs twoway fixed) = (RSS of RSS tf )/(T 1)

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) var(ˆq) = var( ˆβ 1 ) var( ˆβ 0 ) cov( ˆβ 0, ˆq) = 0 Maddala(2001, pp ) 15 k 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

12 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

13 (weighted least square=wls) (self-selection reasons) 16 ANOVA() ANOVA Townsend and Searle (1971) Baltagi and Chang (1994) ANOVA ANOVA (variance component ratio) (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

ANOVA (Searle (1971)Townsend and Searle (1971)Wallace and Hussain (1969)Swamy and Arora (1972)Fuller and Battese

14 (rotating panel ( ) incidental truncation problemheckman ( ) (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) Wooldridge(2002, chap17), pp

2 (FGLS) σv λ i 1 2 σv 2 + T i σµ 2 (48) i y it λ i ȳ i

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)

.., 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,

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

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.

17 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) Breusch-Pagan STATA

darat darat2 ocaprat ss, i(arin) fe xtreg lnrs lnk lnl darat darat2 ocaprat ss, i(arin) re xttest0

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

19 3.2

20 Estimated Coefficient t-statistics Estimated Coefficient z-statistics Ink InL darat darat ocaprat ss _cons 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 F(32, 26156) = Prob>F = chi2(1) = 1.1e + 07 Prob > chi2 = chi2(6) = Prob>chi2 =

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

% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr

1 1. 2014 6 2014 6 10 10% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti 1029 0.35 0.40 One-sample test of proportion x: Number of obs = 1029 Variable Mean Std.