This paper derives a joint Lagrange Multiplier (LM) test which simultaneously tests for the absence of spatial lag dependence and random individual effects in a panel data regression model. It turns out that this LM statistic is the sum of two standard LM statistics. The first one tests for the absence of spatial lag dependence ignoring the random individual effects, and the second one tests for the absence of random individual effects ignoring the spatial lag dependence. This paper also derives two conditional LM tests. The first one tests for the absence of random individual effects without ignoring the possible presence of spatial lag dependence. The second one tests for the absence of spatial lag dependence without ignoring the possible presence of random individual effects.
Baltagi, Badi and Liu, Long, "Testing for Random Effects and Spatial Lag Dependence in Panel Data Models" (2008). Economics Faculty Scholarship. 90.
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