This dissertation consists of two essays on testing hypotheses in panel data models when non-stationarity exists in the model. This is done under the high-dimensional framework where both n (cross-section dimension) and T (time series dimension) are large. In the first essay, I discuss the limiting distribution of the t-statistic; using different panel data estimators and propose using the t-statistic based on Feasible GLS estimator. In the second essay, I develop the bootstrap F-statistic for cross-sectional independence in a panel data model with factor structure.

The first essay considers the problem of hypotheses testing in a simple panel data regression model with random individual effects and serially correlated disturbances. Following Baltagi, Kao and Liu (2008), I allow for the possibility of non-stationarity in the regressor and/or the disturbance term. While Baltagi et al. (2008) focus on the asymptotic properties and distributions of the standard panel data estimators, this essay focuses on test of hypotheses in this setting. One important finding, is that unlike the time series case, one does not necessarily need to rely on the "super-efficient" type AR estimator by Perron and Yabu (2009) to make inference in panel data. In fact, I show that the simple t-ratio always converges to the standard normal distribution regardless of whether the disturbances and/or the regressor are stationary. One caveat is that this may not be robust to heteroskedasticity of the error terms, but it is robust to heterogenous AR parameters across individuals. The Monte Carlo simulations in support of all the results are also provided in this essay.

The second essay discusses testing hypotheses of cross-sectional dependence in a panel data model with an introduction of factor structure. Following Bai (2003, 2004, 2009) and Bai, Kao and Ng (2009), I again allow for the possibility of non-stationarity in the regressor and the factor. I give attention to test of hypotheses using F-tests in this setting. The limiting distribution of F-statistics under the high-dimensional framework has not been derived yet in the literature perhaps because of its theoretical complexity. To circumvent this difficulty, this essay suggests the use of wild bootstrap F-tests based on simulation results under various cases where both regressors and factors can be stationary or non-stationary. The Monte Carlo results show that the bootstrap F-tests perform well in testing cross-sectional independence and are recommended in practice. They have the advantage of being feasible even when we do not observe the factors and do not require for formal theoretical approximations. It is also shown that the bootstrap F-tests are robust to heteroskedasticity but sensitive to serial correlation.