Asymptotically UMP Panel Unit Root Tests

Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.