A Truly Invariant Test for a Unit Root in Generally Trending and Correlated Panels∗

The asymptotic distribution of all unit root test statistics depend on the deterministic specification of the fitted test regression, which need not be equal to the true one. In time series, this implies that different deterministic specifications have their own critical values, whereas in panels, it implies that different specifications have their own mean and variance correction factors. This paper proposes a new panel unit root test that is general enough to accommodate general error serial and cross-section dependence, and a potentially non-linear deterministic trend function. These allowances make the new test one of the most general around. But this is not all. Indeed, what makes the test statistic truly unique is that it is asymptotically invariant to not only the true trend function, but also the deterministic specification of the test regression. This means that the testing is not constrained by the availability of appropriate mean and variance correction factors, thereby enabling inference in situations previously not possible. JEL Classification: C12; C13; C33.