Testing Panel Data Regression Models with Spatial Error Correlation

J23  =  ôtrh^-2 (JT  IN)(IT  (W ⁺ W0

^{2  l}¾°

=  122 tr[JT  (W + W0)] = O;

2¾²

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

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

11  0

1T   0

0  0  2b¾°

0  0   N

using (A.1), we get

√^G2 + N²Th 2:

2(T - 1)        b

where G = u (JT, IN)u — 1 and H = u (IT-W)u as descibed in (2.11).
uu                uu

Appendix A.2: Conditional LM test for λ = O (given ¾² > O)

In this appendix we derive the conditional LM test which tests for no spatial error correlation
given the existence of random regional effects. The null hypothesis is given by Hd: λ = 0
(assuming ¾² > 0). Under the null hyphothesis, the variance-covariance matrix reduces to
0 = ¾2Jτ IN + ¾°INT. It is the familiar form of the one-way error component model, see

Baltagi(1995), with ^-1 = (¾²)^-1(JT IN) + (¾°)^-1(Et IN), where ¾² = T¾² + ¾°.

Under the null hypothesis Hd : λ = 0 (assuming ¾² > 0), we get

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