In 2008 Kelejian extended the J-test procedure to a spatial framework. In that paper he considered a null model which could, but need not, contain spatial lags in both the dependent variable and disturbance term. Under the alternative, he considered one or more non-nested spatial models which could, but need not, also contain spatial lags. Although his suggested test was computationally simple and intuitive, it did not use the available information in an efficient manner.
An Extension of Kelejian's J-Test for Non-Nested Spatial ModelsHarry H. Kelejian and Gianfranco Piras ,
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Regional Science and Urban Economics