This dissertation consists of three essays on testing for cross-sectional dependence and estimation of change points in panel data models. The first two essays discuss two testing procedures of cross-sectional dependence in fixed effects panel data models. In the first essay, I propose a new test for cross-sectional dependence based on the Frobenius norm of the sample covariance matrix of the within residuals. In the second essay, I develop a bias-corrected Lagrange Multiplier (LM) test for cross-sectional dependence in a fixed effects model. In the final essay, I discuss the estimation of change points in a panel data regression model, and establish the consistency and rate of convergence of the change point estimator.

The first essay proposes a new test, called the John test, for cross-sectional dependence of the error terms in linear panel regression models. Different from Pesaran's (2004) CD test and the bias-adjusted LM test (Pesaran et al., 2008), the proposed test is based on a statistic for sphericity of a large dimensional covariance matrix developed by Ledoit and Wolf (2002). Since the errors are unobservable in fixed effects panel models, the within residuals are used. I show that the effect of using the within residuals cannot be ignored asymptotically. The limiting distribution of the proposed test statistic is derived. The Monte Carlo simulations show that the size of the John test is very close to the nominal significance level in large panels.

The second essay discusses the LM test for cross-sectional dependence in fixed effects panel data models. Unlike testing for serial correlation in time series data, Breusch and Pagan's (1980) LM test is not valid for testing cross-sectional dependence in panel data models since the test statistic diverges as the number of cross-sectional units increases. Thus, a scaled version of LM test is proposed by Pesaran (2004). However, this test suffers from a big size distortion and cannot be applied directly in empirical research of panel data with large cross-sectional units, as discussed by Pesaran (2004) and Pesaran, Ullah and Yamagata (2008). This essay finds that, in a fixed effects panel data model, the scaled version of LM test exhibits an asymptotical bias, which is a constant related to the numbers of cross-sectional units and the observations over time. Therefore, a bias-corrected LM test is proposed and its limiting distribution is derived. Additionally, its finite sample properties are examined and compared with the other tests for cross-sectional dependence using Monte Carlo simulations.

The third essay studies the phenomenon of structural change in panel data models. It is a common feature that the processes of GDP, inflation and interest rates, are often vulnerable to political, technological and supply shocks, e.g., the current global financial crisis and the oil crisis in 1970s. Thus, accurate estimation of the change point when the structural change occurs is essential to correct the potentially invalid statistical inference resulting from ignoring this phenomenon. However, the time series literature shows that the estimate of the change point is inconsistent (Picard, 1985; Yao, 1987; Bai, 1994; Bai, 1997; Bai and Perron, 1998). Nevertheless, in panel data models with many individuals, this essay shows that the estimator of the common change point becomes consistent. In addition, the limiting distribution of the change point estimate in panels can be derived without the traditional shrinking break assumption.