On the breitung test for panel unit roots and local asymptotic power

This note analyzes the local asymptotic power properties of a test proposed by Breitung (2000, in B. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels). We demonstrate that the Breitung test, like many other tests (including point optimal tests) for panel unit roots in the presence of incidental trends, has nontrivial power in neighborhoods that shrink toward the null hypothesis at the rate of n^-1/4T^-1 where n and T are the cross-section and time-series dimensions, respectively. This rate is slower than the n^-1/2T^-1 rate claimed by Breitung. Simulation evidence documents the usefulness of the asymptotic approximations given here.