Taking a New Contour: A Novel Approach to Panel Unit Root Tests

The paper introduces a novel approach to testing for unit roots in panels. Following Chang and Park (2004), the approach takes a new contour that is drawn along the line given by the equi-squared-sum instead of the traditional one given by the equi-sample-size. As we show in the paper, the distributions of the unit root tests based on nonlinear IV t-ratios (which includes the Dickey-Fuller test as a special case) are asymptotically normal along the new contour. The normal asymptotics hold under both the null of a unit root and the local-to-unity alternative. Moreover, they are applicable also for the models with intercept or linear time trend, as long as is used the demeaning or detrending method relying only on the past information. Subsequently, we demonstrate that this startling finding may be exploited to invent tools and methodologies for the effective inferences in panel unit root models. In particular, our theory implies that the individual tests may be regarded asymptotically as normal samples if they are computed using the samples having the same sum of squares across all cross-sectional units, which may be obtained through the standard bootstrap method. Consequently, we may conveniently use various functionals of the individual tests to do valid inferences in panels.