An extension of Kelejian's J-test for non-nested spatial models

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.In this paper we suggest a modification of Kelejian's J-test which uses the available information in a more efficient way. We give large sample, as well as small sample Monte Carlo results. Perhaps counter to intuition, we also demonstrate that the “J-test procedure” cannot be used to establish a test for the structure of the error term.