Testing Panel Data Regression Models with Spatial Error Correlation

@F° ^lH^a

a¾≡ ^lH^a

@Â H"

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

1 1 1 u~⁰ u~

^- Q^tr[ 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∂μ_ssi = 2trh -1(@ _u=aμ_r´ -1(@ _u=aμ_β´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 = 2^tr[⅛⁽^I^t^Iⁿ)H = 2¾4;

@²L 1 1 2 NT²

J²² = El^- J = 2^tr⅛⁽^J^t^Iⁿ)J = ι¾τ;

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

= 1 tr[I_τ (2W² + 2W ⁰W )] = Tb;

1 1 1 NT

J¹² =2^tr ⅛ (I^T I^N ) ¾° ⁽J^T IN )J = 2¾° ’

J13 = 1 trh A (It In )(It (W + W ⁰))i

²^l¾° -ⁱ

= TT¹₂ tr[Iτ (W + W⁰)] = 0;

2¾²

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