Testing Panel Data Regression Models with Spatial Error Correlation

misleading inference. Next, two conditional LM tests are derived. One for the existence of
spatial error correlation assuming the presence of random region effects, and the other for the
existence of random region effects assuming the presence of spatial error correlation. These
tests guard against misleading inference caused by (i) one directional LM tests that ignore
the presence of random region effects when testing for spatial error correlation, or (ii) one
directional LM tests that ignore the presence of spatial correlation when testing for random
region effects.

Section 2 revisits the spatial error component model considered in Anselin (1988) and provides
the joint and conditional LM tests proposed in this paper. Only the final LM test statistics
are given in the paper. Their derivations are relegated to the Appendices. Section 3 compares
the performance of these LM tests as well as the corresponding likelihood ratio LR tests using
Monte Carlo experiments. Section 4 gives a summary and conclusion.

2 THE MODEL AND TEST STATISTICS

Consider the following panel data regression model, see Baltagi (2001):

yti = X'tiβ + Uti; i = 1;..;N ; t =1; ... ;T;                                                  (2.1)

where y_ti is the observation on the ith region for the tth time period, X_ti denotes the kx1
vector of observations on the non-stochastic regressors and u_ti is the regression disturbance.
In vector form, the disturbance vector of (2.1) is assumed to have random region effects as
well as spatially autocorrelated residual disturbances, see Anselin (1988):

^ut = M ^{+ e}t;                                                                                       (2.2)

with

^et = ^χW<.t + °t;                                                                                  (2.3)

where ut = (uti; : : : ; utN), et = (e_ti; ::: ; CtN) and μ' = (μ₁,... ; μN) denote the vector of
random region effects which are assumed to be IIN(0; ¾^). X is the scalar spatial autoregres-
sive coe¢cient with j λ j< 1: W is a known N £ N spatial weight matrix whose diagonal
elements are zero. W also satisfies the condition that (In — XW) is nonsingular for all j λ j< 1.
°t = (°ti;... ; °tN); where °ti is i:i:d: over i and t and is assumed to be N(0; ¾°): The f°tig
process is also independent of the process fμ_ig. One can rewrite (2.3) as

et = (In — XW )-1°t = B^-1° t;                                                      (2.4)

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