This article studies tail behavior for the error components in the stochastic frontier model, where one component has bounded support on one side, and the other has unbounded support on both sides. Under weak assumptions on the error components, we derive nonparametric tests that the unbounded component distribution has thin tails and that the component tails are equivalent. The tests are useful diagnostic tools for stochastic frontier analysis. A simulation study and an application to a stochastic cost frontier for 6,100 US banks from 1998 to 2005 are provided. The new tests reject the normal or Laplace distributional assumptions, which are commonly imposed in the existing literature.