Summary We propose simple and robust diagnostic tests for spatial error autocorrelation and spatial lag dependence. The idea is to reformulate the testing problem such that the outer product of gradients (OPG) variant of the LM test can be employed. Our versions of the tests are based on simple auxiliary regressions, where ordinary regression t- and F-statistics can be used to test for spatial autocorrelation and lag dependence. An important advantage of the proposed test statistics is that they are robust against heteroscedastic errors. Therefore, our approach gives practitioners an easy to implement and robust alternative to existing tests.