Empirical behaviour of Anselin et al.’s locally robust LM tests for spatial dependence in a panel data setting

A key issue in spatial models is to appropriately specify the spatial effect. Robust Lagrange Multipliers (RLM) tests have long been popular in spatial econometrics for discriminating between spatial lag and spatial error processes. A review of the recent applied literature shows how they are often (mis)applied in a panel context, where further issues arise the tests were not designed to address in the first place: individual or time heterogeneity and time persistence. We address the performance of RLM tests in spatial panels through Monte Carlo simulation showing that they can become virtually useless as a specification device under substantial individual and especially time heterogeneity, regardless whether correlated or not; or in the presence of spatially lagged regressors. Accounting for unobserved effects by demeaning the data or adding dummies restores the good properties of the RLM. The presence of spatially lagged regressors remains instead problematic. We conclude with suggestions for improving applied practice.