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, Model(0), 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 g = 1, in this paper we examine the finite sample properties of a spatial J statistic that is asymptotically chi(2)(2) under the null, and an alternative version that is conjectured to be approximately chi(2)(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.