Subsampling Hypothesis Tests for Nonstationary Panels with Applications to the PPP Hypothesis

This paper studies subsampling hypothesis tests for panel data that are possibly nonstationary, and cross-sectionally correlated and cross-sectionally cointegrated. The tests include panel unit root and cointegration tests as special cases. The number of cross-sectional units in the panel data is assumed to be finite, and that of time series observations infinite. Cross-sectional correlation is allowed for both regressors and error terms. Two types of subsampling, non-centered and centered, are considered. It is shown that empirical distributions using subsamples uniformly converge to corresponding limiting distributions. For the non-centered subsampling, the result is shown in the mode of almost sure convergence and discontinuous limiting distributions are allowed. For the centered subsampling, the uniform convergence result is obtained in the mode of convergence in probability and only for continuous limiting distributions. Test consistency using the critical values from the empirical distributions is also established. These results are applied to panel unit root and stationarity tests. The panel unit root tests considered are Levin, Lin and Chu (2002)'s t-test, Im, Pesaran and Shin's (2003) averaged t-test and Choi's (2001) Z test. For the null of stationarity, Hadri's (2000) test is used. Block sizes of subsamples are chosen by stochastic calibration. Simulation results show that the subsampling distributions of the panel unit root tests using the stochastic calibration provide reasonably good approximations to the finite sample distributions of the tests.