Panel LM Unit Root Tests with Trend Shifts

This paper proposes a new Lagrange multiplier (LM) based unit root test for panel data allowing for heterogeneous structural breaks in both the intercept and slope of each cross-section unit in the panel. We note that panel unit root tests allowing for breaks in the slope will critically depend on the nuisance parameters indicating the size and location of breaks. Any panel tests that ignore this dependency on the nuisance parameter will be subject to serious size distortions. To address this problem, our test employs a method that renders the asymptotic distribution of the panel tests invariant to nuisance parameters. We derive the asymptotic properties of our test and also examine its finite-sample properties. In addition, our test easily can be modified to correct for the presence of cross-correlations in the innovations of the panel. We illustrate this by applying the cross-sectionally augmented ADF (CADF) procedure of Pesaran (2007) to our test statistic