Model Checking in Partially Linear Spatial Autoregressive Models

This article proposes two new classes of nonparametric tests for the correct specification of linear spatial autoregressive models based on the "integrated conditional moment" approach. Our test statistics are constructed as continuous functionals of a residual marked empirical process as well as its projected version. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives. The proposed tests do not involve the selection of tuning parameters such as bandwidths and are able to detect a broad class of local alternatives converging to the null at the parametric rate n−1/2, with n being the sample size. We also propose a multiplier bootstrap procedure that is computationally simple to approximate the critical values. Monte Carlo simulations illustrate that our tests have a reasonable size and satisfactory power for different types of data-generating processes. Finally, an empirical analysis of growth convergence is carried out to demonstrate the usefulness of the tests.