Testing Panel Data Regression Models with Spatial Error Correlation

and

2 TNN NN tr[(W⁰B + B'W) + (B⁰B)^-1]

rτι _ -^- -^- -I

ɪ tr[2b⁰2b]

Jμ =

T ^t tr[((W ⁰B + Bb⁰W ) + (_jb⁰ B?)^-1^¢² ]

rr> . ^ ^.

2T2 tr[W ⁰B + B^fW ]
^°

⁷ ; (2.28)

2¾4 tr[(ib⁰ib)²] J

T
2¾°

N ¾° g h
24 2

¾°g ¾° c ¾° d
h ¾° d Te

(2.29)

where g = tr[(W⁰B + Bb⁰W)(B⁰B) 1], h = tr[B⁰B], c = tr
. ^ - - , ^. ^ .ï-

tr[W⁰B^b + B^b⁰W] and e = tr[(B^b⁰B^b)²]. Therefore,

((W ⁰B + B⁰W )(B⁰B)-1)

LMμ = (D)μ)²^²¾°^TNσ°ec - N¾°d² - Tσ°g²e + 2¾°ghd - ¾°h²c)

(≡°c - ¾°g²^ (2.30)

where D_μ and J_μ are evaluated at the maximum likelihood estimates under the null hypoth-
esis H0e. However, LM_μ ignores the fact that the variance component cannot be negative.
Therefore, the one-sided version of this LM test is given by

D_μJ(2¾,=T)(N¾°c - ¾°g²)

(2.31)

LMμ = ^V _

∙ξ=TN¾°ec - N¾°d² - T¾°g²e + 2¾°ghd - ¾°h²c

and this should be asymptotically distributed as N(0; 1) under He as N ! 1 for T fixed.

3 MONTE CARLO RESULTS

The experimental design for the Monte Carlo simulations is based on the format extensively
used in earlier studies in the spatial regression model by Anselin and Rey (1991) and Anselin
and Florax (1995) and in the panel data model by Nerlove (1971).

The model is set as follows :

^yit = ® + ^x'i_tβ + uit; i = ¹^,∙ ∙ ∙ N; t = 1,∙ ∙ ∙ ; T; (3.1)

where ® = 5 and β = 0:5. x_it is generated by a similar method to that of Nerlove (1971). In
fact, xi_t = 0:1t + 0:5xi_;t_-1 +zi_t, where zi_t is uniformly distributed over the interval [-0:5; 0:5].
The initial values xio are chosen as (5 + 1Ozio). For the disturbances, u_it = μ_i + "_it, "_it =
λ pN=1 Wij "it + ° it with μ_i » IIN (0, ¾μ) and °it » IIN (0,¾° ): The matrix W is either a

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