rook or a queen type weight matrix, and the rows of this matrix are standardized so that they
sum to one.1 We fix ¾X + ¾° = 20 and let ½ = ¾X=(¾X + ¾°) vary over the set (0; 0:2; 0:5; 0:8).
The spatial autocorrelation factor λ is varied over a positive range from 0 to 0:9 by increments
of 0:1. Two values for N = 25 and 49, and two values for T = 3 and 7 are chosen. In total,
this amounts to 320 experiments.2 For each experiment, the joint, conditional and marginal
LM and LR tests are computed and 2000 replications are performed. In a first draft of this
paper we reported the two-sided LM and LR test results to show how misleading the results
of these tests can be. These results are available upon request from the authors. In this
version, we focus on the one-sided version of these tests except for testing H0: ¾X = 0 where
we thought a warning should be given to applied econometricans using packages that still
report two-sided versions of this test.
3.1 Joint Tests for H0a: λ = ¾2 = 0
O
Table 1 gives the frequency of rejections at the 5% level for the handy one-sided Honda-type
LM test statistic LMH given in (2.18), the GHM test statistic given in (2.19) and LRJ given
in (2.23). The results are reported for N = 25; 49 and T = 3; 7 for both the Queen and Rook
weight matrices based on 2000 replications. Table 1 shows that at the 5% level, the size of
the joint LR test (LRJ) is not significantly different from 0:05 for all values of N and T and
choice of the weight matrix W . The same is true for LMH and GHM except for N = 25 and
T = 3 where they are undersized. The power of all three tests is reasonably high as long as
A > 0:3 or ½ > 0:2. In fact, for ½ ≥ 0:5 this power is almost one in all cases. For a fixed A or
½, this power improves as N or T increase.
1 The weight matrix with first-order contiguity according to the rook criterion has the cells immediately
above, below, to the right, and to the left, for a total of four neighboring cells. The weight matrix with first
order contiguity according to the queen criterion is eight cells immediately surrounding the central cell, see
Anselin and Rey (1991).
2The Monte Carlo experiments were also run for negative λ ranging between -0.1 and -0.9. The results
were similar and are not reproduced here to save space.
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