Testing for unit roots on heterogeneous panels: A sequential approach

The is a growing trend of criticism against the use of panel data unit root test for assessing hypotheses such as the purchasing power parity. The usual argument of a gain in power with respect to univariate unit root tests is not relevant as different nulls are involved when testing on panel data. In the context of a comparative, multi-country, study, inference based on individual unit root tests suffers mainly from a huge size distortion, even more than from low power. When the null hypothesis is -as usually in comparative research- a number of countries for which the variable of interest follows a unit root process, we propose to adopt a sequential strategy, as a way to combine a rigourous control over the size with the search for satisfactory power. We show how usual statistics have to be adapted, and we illustrate the implementation of this strategy both through simulation and through an empirical application to the PPP hypothesis within the OECD countries.