This paper concerns linear models for grouped data with group-specific effects. We construct a test for the null of no within-group correlation beyond that induced by the group-specific effect. The approach tests against correlation of arbitrary form while allowing for (conditional) heteroskedasticity. Our setup covers models with exogenous, predetermined, or endogenous regressors. We provide theoretical results on size and power under asymptotics where the number of groups grows but their size is held fixed. In simulation experiments we find good size control and high power in a wide range of designs. We also find that our test is more powerful than the popular test developed by Arellano and Bond (1991), which uses only a subset of the information used by our procedure.