Testing Panel Data Regression Models with Spatial Error Correlation

@L|

∂λ ^lHe

+ 212 ^u[IT

(W⁰Bb + Bb⁰W)]u^ = 0;

-1

u

∂λ ^lHe

⅛_v ¹T
. ^ ^

B'B) ⁽b°IT  (B'B)^-1(W0B + B'W)(^b'B)^-1)

=IT  (W⁰Bb+Bb⁰W)(Bb⁰Bb)

-1

-¹  ∖  -¹Le = ¾2IT  (W'B + B'w):

Therefore, the score vector under H₀^e is given by

ʌ

D^{^} =

0

0

ʌ

D^ _μ

The elements of the information matrix for this model using (A.5) are given by

@²L       1     2 -1       2   TN

J¹¹   El @(σ°)²J^lHe   2 [((^σ°)  IT   IN)]    2b° ;

J22  = E h - @2LLi|   = ¹ tr [(It  (W'B + B'W)(B'B)^-1)²i

L @\ -^llHe 2 L                                         J

= T tr[⁽(W 'b + B'w )(B'B)^-1)2i ;

J33 = Eh^- @2L] IH₅ =^{1 tr[((b2)-1} JT  b^Bi = 2Tb°^tr[(B'^B)2]'

J12

@²L   l 1

E[^- @ст°@Л] ^lHe = 2^trh(b°)^ ^(IT   IN^)(IT

1

-tr ^(b° )^-1IT   (W 'B + B^,W )(B'B)^-1)J

(W^'Bb + Bb^' W)(Bb^'Bb)^-1

(A.30)

T

—2 tr (W'B + B^fW)(B'B)^-1∖ ;

²¾° ^{l                            j}

@²L        1

J13 = E^{[ -} â^^]|He = 2^tr[(b°)^-1(IT  IN)((^b2)  JT  B B

°    pt      0

1T

2¾4 tr [JT  B ^b] = 2¾4^tr[B B^];

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