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The tests rely on suitably weighted residual cross\u2010covariances or cross\u2010correlations, and are in this sense a generalization of Pesaran's (2004, CESifo working paper 1229) test for no cross\u2010sectional dependence. They follow chi\u2010squared distributions under joint <jats:italic>N<\/jats:italic>,<jats:italic>T<\/jats:italic> asymptotics without restrictive sphericity or distributional assumptions. When using the outcome of the directed tests to decide whether to use panel\u2010robust standard errors or not for testing slope parameters, the latter tests are apparently not affected; they can be severely affected, though, if using generic cross\u2010correlation tests as pretests. 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