This paper considers a general heteroskedastic error component model using panel data, and derives a joint Lagrange multiplier (LM) test for homoskedasticity against the alternative of heteroskedasticity in both error components. It contrasts this joint LM test with marginal LM tests that ignore the heteroskedasticity in one of the error components. Monte Carlo results show that misleading inference can occur when using marginal rather than joint tests when heteroskedasticity is present in both components.