Unit root tests for cross-sectionally dependent panels: The influence of observed factors

• We consider a panel unit root model with cross-sectional dependence.
• The cross-sectional dependence is generated by an observed factor.
• We show that the model is Locally Asymptotically Mixed Normal (LAMN).
• We derive the asymptotic local power function of three tests with optimal features.
• We recommend the use of a tt-test in applications.

This paper considers a heterogeneous panel unit root model with cross-sectional dependence generated by a factor structure—the factor common to all units being an observed covariate. The model is shown to be Locally Asymptotically Mixed Normal (LAMN), with the random part of the limiting Fisher information due to information generated by the covariate. Because of the LAMN structure, no asymptotically uniformly most powerful test exists; we investigate the asymptotic power properties of the locally optimal test, the best point optimal test, and the conditionally optimal tt-test. Although one might expect the best point optimal test to be superior, the performance of the computationally simpler tt-test is comparable.