Asymptotically UMP panel unit root tests: the effect of heterogeneity in the alternatives

In a Gaussian, heterogeneous, cross-sectionally independent panel with inciden- tal intercepts, Moon, Perron, and Phillips (2007) presents an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon, Perron, and Phillips (2007), a pooled GLS based-test using the Breitung and Meyer (1994) device, and a new test based on the asymptotic structure of the model, are all asymptotically UMP. Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.