# Three Essays on Panel Data Analysis

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## Abstract

This dissertation analyzes cross-sectional dependence, identification of common factors, and convergence in panel data. It is consists of three chapters. The first chapter studies asymptotic comparison among pre-testing procedures. Empirical researchers should decide which regression should be run at the beginning of their studies. There are two regressions for panel data analysis: two-way fixed effects regression (with individual and year fixed effects) and so-called factor augmented regression. If the two-way fixed effects regression fails to eliminate cross-sectional dependence, then the factor augmented regression should be used instead. Two pre-testing procedures are mainly available in the literature: the use of the number of common factors and the direct test of the factor loading coefficients. This chapter compares the pre-testing procedures asymptotically. When the true slope coefficients are homogeneous (βi = β), the two methods suggest the same estimators. Under the heterogeneous factor loadings, both pre-testing procedures suggest running the factor augmented regression. Meanwhile under the homogeneous factor loadings, two methods suggest running the two-way fixed effects regression. In this chapter, we discover that the two-way fixed effects regression gives more efficient estimation than the one of the factor augmented regressions when the slope coefficients are homogeneous with homogeneous factor loadings. By means of Monte Carlo simulations, the asymptotic claims are verified. We also provide an empirical example to describe how to use the two pre-testing procedures. The second chapter proposes a novel but simple method to identify unknown common factors that have either stochastic trends or just trend components with a convergent panel. Typically, the weak σ-convergence test requires the elimination of common components before the test is performed. Instead, this chapter uses potential variables to eliminate common (non)-stochastic trending factors, and if the left-over terms are weakly σ-converging, then the variables can be identified as unknown common factors. This chapter provides the asymptotic properties of the suggested method, and examines finite sample performances by Monte Carlo simulations. To demonstrate how to use the new procedure, this chapter identifies the underlying common factor for 46 disaggregate PCE inflation rates. Among many potential macro variables, only the Federal Funds rate becomes the common factor. In the last chapter, I propose a new approach to the relative convergence test. The original relative convergence test proposed by Phillips and Sul (2007) recommends discarding the first 1/3 of the time series data to achieve the best performance in terms of the size and power of the test. My new approach to the relative convergence test does not require discarding any time series data by assuming the unobservable data is already discarded. In this chapter, I compare the new approach to the Phillips and Sul (2007)’s test and determine, through a Monte-Carol simulation, at what fraction the new approach achieves the best performance in terms of size and power of the test. I confirm that the new approach performs better than the original approach when the fraction is set 1/10 of a penalty function. To compare my new method to the Phillips and Sul (2007) method, I provide an empirical example using U.S. Per Capita Personal Income data to compare my new method to the Phillips and Sul (2007)’s method.