Testing Panel Data Regression Models with Spatial Error Correlation

J12 = E h - @@@ ■'i = 2^teh((¾Γ²JT + ¾-²Et)  InK²(Jt  In)]        (A.19)

- °-' Ц-     —

_ NT

= 2¾4^,

J13 = Eh - a¾₂Lλi = 24((¾1^²JT + ¾-²ET)  In)

((¾^-2Jr + -^-2Et )  In )(-° It  (W + W ⁰))i = 0,

@²L

E [^-@ 2 ∂λ J = 2 tr ¾1²(JT  In )((¾ι2^tJτ + ¾°ET )   In )

n

2

(¾° It  (W + W ⁰))i = -° tr h 14J Jt  (W + W ⁰)i = 0,

2    ¾₁

where the result that J13 = J23 = 0 follows from the fact that the diagonal elements of W is
0 and J33 uses the fact that tr(W²) = tr(W⁰²), and b = tr(W ² + W⁰W).

Therefore, the information matrix evaluated under H₀^d is given by

as described in (2.24).

Appendix A.3: Conditional LM test for ¾² = 0 (assuming ʌ = 0)

This appendix derives the conditional LM tests for zero random regional effects assuming that
spatial error correlation exists. We give the detailed derivation of the score and information
matrix for testing H₀^e : -²_n = 0 (assuming A 6= 0).

Under H₀^e,

0  =  -° It   (B⁰B)^-1,

-¹  =  ^12 It   (B⁰B),

²

23

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