Three Essays on Panel Data Analysis

The first chapter, Two-Way Fixed Effects versus Panel Factor Augmented Estimators: Asymptotic Comparison among Pre-testing Procedures, provides asymptotic analyses of pretesting procedures when the slope coefficients are heterogeneous across cross-sectional units. Empirical researchers may wonder whether or not a two-way fixed effects estimator (with individual and time fixed effects) is sufficiently sophisticated to isolate the influence of common shocks on the estimation of slope coefficients. If it is not, practitioners need to run the so-called panel factor augmented regression instead. There are two pre-testing procedures available in the literature: the use of the estimated number of factors and the direct test of estimated factor loading coefficients. This chapter compares the two pre-testing methods asymptotically. Under the presence of the heterogeneous factor loadings, both pre-testing procedures suggest using the Common Correlated Effects (CCE) estimator. By comparing asymptotic variances, this chapter finds that when the slope coefficients are heterogeneous with homogeneous factor loadings, the CCE estimation is, surprisingly, more efficient than the two-way fixed effects estimation. The second chapter, A New Test for Slope Homogeneity in a Panel Regression with Interactive Fixed Effects, proposes a new test for slope homogeneity in a panel regression with interactive fixed effects without any restriction on the relative expansion rate of n, the number of cross-sectional units, and T, the number of periods.This test is based on a comparison of the estimated number of common factors from two regression residuals. The first regression is an unconstrained regression with heterogeneous slope parameters. The second regression is a pooled regression based on the principal components mean group method. Under the slope heterogeneity, this chapter shows that the estimated number of common factors from the first regression residuals is asymptotically smaller than that of the second regression residuals. In the third chapter, Identification of Outliers for Testing Weak σ-Convergence, the authors suggest three novel procedures for separating the divergent series from a convergent club. Weak σ−convergence test is designed to detect whether cross-sectional variances of a panel data of interest show consistent diminution over time. When the panel data of interest includes divergent series, the cross-sectional variances become contaminated, which results in a seemingly divergent behavior. This chapter deals with this problem. We propose three novel detection procedures for identifying divergence series and provide the asymptotic justification. Utilizing Monte Carlo simulations, the finite sample properties are examined. We demonstrate the effectiveness of the newly proposed methods by using infant mortality rates in 42 countries. Even though all infant mortality rates have shown a downward trending behavior over time, the cross-sectional variance of log infant mortality rates is diverging over time. By using the proposed sieving methods, we identify six outliers. After excluding these outliers, the rest of the infant mortality rates are weakly σ-converging over time. Altogether, this dissertation provides methods for a better understanding of the source and nature of the cross-sectional dependence in panel data models.