Specifying spatial effects in panel data: Locally robust vs. conditional tests

We address the issue of specifying a spatial lag vs. spatial error process in spatial panel models. The popular locally robust Lagrange multiplier (RLM) tests for spatial lag vs. error are compared to optimal alternatives based on maximum likelihood estimation: Wald and likelihood ratio (LR) tests requiring estimation of the full encompassing model, and conditional Lagrange multiplier (CLM) tests drawing on the reduced specification. Monte Carlo simulations are performed in a typical spatial panel context. Individual effects are successfully eliminated through the forward orthogonal deviations transformation, making the RLM suitable for panel data. Nevertheless, the statistical properties of Wald and LR are superior to those of the RLM. The CLM also dominates the RLM, as long as the sample is at least of moderate size. The RLM are computationally very convenient, but ML-based tests are feasible in most usage cases on mainstream hardware.