A panel unit root test in the presence of cross-section dependence

A panel unit root test is derived based on a Lagrangian Multiplier for panels with a cross-section dependence modeled using factor models. The test statistic is shown to be different from square of test statistic of Pesaran (2007) even for a case of no constant and no trend, hence the test statistic is not simply a different calculation of the suggestion made in Pesaran (2007). Implementation of the test is very simple and it is easy to understand its mechanics. Furthermore, the limiting distribution of of individual cross-sectionally augmented test statistics which appear to be functions of standard wiener processes are shown to be free of nuisance parameters. The critical values of the proposed test statistics are tabulated. The small sample size properties of the proposed test statistics are shown to outperform the suggestion of Pesaran (2007) in terms of power, in many cases, i.e. the proposed test statistic is more powerful, in particular, for alternatives involving some individuals with unit root and some with stationary behaviors, which makes it quite appealing for practical purposes. The asymptotics are established under N/T → δ > 0 with N being the number of cross-sections and T the length of time series.