Testing Panel Data Regression Models with Spatial Error Correlation

This LM2 test statistic should be asymptotically distributed as N(0; 1) under H₀^c.  The

corresponding standardized LM (SLM) test statistic is given by

where d2 = —-— and D2 = (It  W). Under H∩; SLM2 should be asymptotically distrib-

u~⁰ u~

uted as N(0; 1). SLM2 should have asymptotic critical values that are generally closer to the

corresponding exact critical values than those of the unstandardized LM2 test statistic.

2.4 One-Sided Joint LM Test for Ha: λ = ¾2, = 0

0

Following Honda (1985) for the two-way error component model, a handy one-sided test
statistic for Ha : λ = ¾X = 0 is given by

LM H = (LM₁ + LM2)=p2;                                             (2.18)
which is asymptotically distributed N(0; 1) under H₀^a.

Note that LMi in (2.12) can be negative for a specific application, especially when the true
ariance component ¾²_x is small and close to zero. Similarly, LM2 in (2.16) can be negative
especially when the true A is small and close to zero. Following Gourieroux, Holly and
Monfort (1982), here after GHM, we propose the following test for the joint null hypothesis
H^a
H0:

Under the null hypothesis H₀^a , ²_m has a mixed ²- distribution:
Âm » ⁽4)Â^{2(0) + (}2)Â^{2(1) + (}4)²⁽²⁾;

where â²(0) equals zero with probability one. The weights (4 ); (∣) and (4 ) follow from the
fact that LM1 and LM2 are asymptotically independent of each other and the results in
Gourieroux, Holly and Monfort (1982). The critical values for the mixed ²_m are 7:289, 4:321

and 2:952 for ® = 0:01, 0:05 and 0:1, respectively.

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