Finite Sample Distributions and Non-normality in Second Generation Panel Unit Root Tests

As a remarkable advantage, panel unit root testing statistics present Gaussian distribution in the limit rather than the complicated functionals of Wiener processes compared with traditional single time series tests. Therefore, the asymptotic critical values are directly used and the finite sample performance is not given proper attention. In addition, the unit root test literature heavily relies on the normality assumption, when this condition fails, the asymptotic results are no longer valid. This thesis analyzes and finds serious finite sample bias in panel unit root tests and the systematic impact of non-normality on the tests. Using Monte Carlo simulations, in particular, the application of response surface analysis with newly designed functional forms of response surface regressions, the thesis demonstrates the trend patterns of finite sample bias and test bias vary closely in relation to the variation in sample size and the degree of non-normality, respectively. Finite sample critical values are then proposed, more importantly, the finite sample critical values are augmented by the David-Johnson estimate of percentile standard deviation to account for the randomness incurred by stochastic simulations. Non-normality is modeled by the Lévy-Paretian stable distribution. Certain degree of non-normality is found which causes so severe test dis-tortion that the finite sample critical values computed under normality are no longer va-lid. It provides important indications to the reliability of panel unit root test results when empirical data exhibit non-normality. Finally, a panel of OECD country inflation rates is examined for stationarity considering its feature of structural breaks. Instead of constructing structural breaks in panel unit root tests, an alternative and new approach is proposed by treating the breaks as a type of non-normality. With the help of earlier results in the thesis, the study supports the presence of unit root in inflation rates.