On the interpretation of panel unit root tests

Applications of panel unit root tests have become commonplace in empirical economics, yet there are ambiguities as how best to interpret the test results. This note clarifies that rejection of the panel unit root hypothesis should be interpreted as evidence that a statistically significant proportion of the units are stationary. Accordingly, in the event of a rejection, and in applications where the time dimension of the panel is relatively large, it recommends the test outcome to be augmented with an estimate of the proportion of the cross-section units for which the individual unit root tests are rejected. The economic importance of the rejection can be measured by the magnitude of this proportion. © 2012 Elsevier B.V. All rights reserved. Over the last decade, considerable work has been carried on unit root testing in panel data models. See, for example, Breitung and Pesaran (2008) for a recent survey of the literature. Most panel unit root tests are designed to test the null hypothesis of a unit root for each individual series in a panel. The formulation of the alternative hypothesis is however a controversial issue that critically depends on which assumptions one makes about the nature of the homogeneity/heterogeneity of the panel. A number of panel unit root tests proposed in the literature use the following articulation of the alternative hypothesis: Ha 1 : each of the series is stationary as a panel, while other tests use Hb 1 : at least one of the series in the panel is generated by a stationary process. The above two formulations of the alternative hypothesis are not satisfactory for carrying inference on the non-stationarity properties of panel data models. To see why this is so, consider the following simple dynamic heterogeneous panel on N crosssections observed over T time periods: yit = (1 − φi) μi + φiyi,t−1 + εit , i = 1, 2, . . . ,N; t = 1, 2, . . . , T , (1) ✩ Helpful suggestions by Michael Binder, Ron Smith, and Elisa Tosetti are gratefully acknowledged. ∗ Tel.: +44 213 304 6897. E-mail address:[email protected]. 0165-1765/$ – see front matter© 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2012.04.049 where initial values, yi0, are assumed to be given. (1) can be expressed as ∆yit = ci + βiyi,t−1 + εit , (2) where ci = (1 − φi) μi, βi = −(1 − φi) and ∆yit = yit − yi,t−1. The null hypothesis of unit roots can then be written as H0 : βi = 0 for all i. (3) Under a homogeneous alternative we have βi = β ≠ 0 for all i, and