Testing Panel Data Regression Models with Spatial Error Correlation



@L

@F° lHa

@L

a¾≡ lHa

M

@L

H"


- 1tr⅛ (It (B0BF1 )] + 1[~ (It (B0B)"1)~],
2 ¾°                   2 ¾4

1  1      1 u~0 u~

- Qtr[ 2 INT] + F^4^] = 0;

2 ~°        2 ¾ °


2 _ NT ,U0(Jτ  In)U

M) = 2¾° '     U0U


D(A) =


NT U0 (IT
^^2


-1;


(w + W0))~ = NTU0(Iτ  w)u

U~0 U~                U~0 U~


Therefore, the score with respect to μ, evaluated at the restricted MLE is given by

203

20

D~ μ =

666 D(¾~2M)

7=

NT u ~0(Jτ IN)u _ 1 ∖
2¾° ×     u0u

L D(~) J

^NTr U0 (IT ^W)u

u0 u


(A.4)


For the information matrix, it is useful to use the formula given by Harville(1977):

Jrs = Eh - 2L=∂μr∂μssi = 2trh -1(@ u=aμr´ -1(@ u=aμβ´i,

(A.5)


for r; s = 1; 2; 3. The corresponding elements of the information matrix are given by

J11 = E h -


@2l 1 ι.\( ι (T ɪ й2]   nt

a(¾°)2J = 2tr[⅛(It In)H = 2¾4;

@2L    1  1       2   NT2

J22 = El- J = 2tr(Jt  In)J = ι¾τ;

J33 = E h - @2L i =2 trh~Iτ  (W + W 0)2i

=  1 tr[Iτ  (2W2 + 2W 0W )] = Tb;

1  1        1          NT

J12 =2tr(IT  IN ) ¾° (JT  IN )J = 2¾°

J13  =  1 trh A (It  In )(It  (W + W 0))i

2    l¾°                                         -i

=  TT12 tr[Iτ   (W + W0)] = 0;

2¾2

20



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