Bootstrap inference in spatial econometrics : the J test

Kelejian (2008) introduces a J-type test for the situation in which a null linear regression model, Model0, is to be tested against one or more rival non-nested alternatives, Model1, . . ., Modelg, where typically the competing models possess endogenous spatial lags and spatially autoregressive error processes. Concentrating on the case g1, in this paper we examine the finite sample properties of a spatial J statistic that is asymptotically x2 2 under the null, and an alternative version that is conjectured to be approximately x2 1; both introduced by Kelejian. We demonstrate numerically that the tests are excessively liberal in some leading cases and conservative in others using the relevant chi-square asymptotic approximations, and explore how far this may be corrected using a simple bootstrap resampling method.