Unit root inference in panel data models where the time-series dimension is fixed: A comparison of different tests

The objective of the paper is to investigate and compare the performance of some of the unit root tests in micro-panels which have been suggested in the literature. The framework is an autoregressive panel data model allowing for heterogeneity in the intercept but not in the autoregressive parameter. The tests being considered can be used to distinguish between the null hypothesis of each time-series process being a random walk and the alternative hypothesis of each time-series process being stationary with individual-specific levels but the same autoregressive parameter. In addition, the tests are all based on usual t-statistics corresponding to least squares estimators of the autoregressive parameter resulting from different transformations of the model. The performance of the tests is investigated by deriving the local power of the tests when the autoregressive parameter is local-to-unity. The results show that the assumption concerning the initial values is important in this matter. The outcome of a simulation experiment demonstrates that the local power of the tests provides a good approximation to their actual power in finite samples.